Control of microtubule dynamics and length by cyclin A- and cyclin B-dependent kinases in Xenopus egg extracts

Switching from weak to strong cortical attachment of microtubules accounts for the transition from nuclear centration to spindle elongation in metazoans

The centrosome is a major microtubule organizing center in animal cells. The position of the centrosomes inside the cell is important for cell functions such as cell cycle, and thus should be tightly regulated. Theoretical models based on the forces generated along the microtubules have been proposed to account for the dynamic movements of the centrosomes during the cell cycle. These models, however, often adopted inconsistent assumptions to explain distinct but successive movements, thus preventing a unified model for centrosome positioning. For the centration of the centrosomes, weak attachment of the astral microtubules to the cell cortex was assumed. In contrast, for the separation of the centrosomes during spindle elongation, strong attachment was assumed. Here, we mathematically analyzed these processes at steady state and found that the different assumptions are proper for each process. We experimentally validated our conclusion using nematode and sea urchin embryos by manipulating their shapes. Our results suggest the existence of a molecular mechanism that converts the cortical attachment from weak to strong during the transition from centrosome centration to spindle elongation.

Measuring Mitotic Spindle and Microtubule Dynamics in Marine Embryos and Non-model Organisms

During eukaryotic cell division a microtubule-based structure, the mitotic spindle, aligns and segregates chromosomes between daughter cells. Understanding how this cellular structure is assembled and coordinated in space and in time requires measuring microtubule dynamics and visualizing spindle assembly with high temporal and spatial resolution. Visualization is often achieved by the introduction and the detection of molecular probes and fluorescence microscopy. Microtubules and mitotic spindles are highly conserved across eukaryotes; however, several technical limitations have restricted these investigations to only a few species. The ability to monitor microtubule and chromosome choreography in a wide range of species is fundamental to reveal conserved mechanisms or unravel unconventional strategies that certain forms of life have developed to ensure faithful partitioning of chromosomes during cell division. Here, we describe a technique based on injection of purified proteins that enables the visualization of microtubules and chromosomes with a high contrast in several divergent marine embryos. We also provide analysis methods and tools to extract microtubule dynamics and monitor spindle assembly. These techniques can be adapted to a wide variety of species in order to measure microtubule dynamics and spindle assembly kinetics when genetic tools are not available or in parallel to the development of such techniques in non-model organisms.

Cytoplasm mechanics and cellular organization

As cells organize spatially or divide, they translocate many micron-scale organelles in their cytoplasm. These include endomembrane vesicles, nuclei, microtubule asters, mitotic spindles, or chromosomes. Organelle motion is powered by cytoskeleton forces but is opposed by viscoelastic forces imparted by the surrounding crowded cytoplasm medium. These resistive forces associated to cytoplasm physcial properties remain generally underappreciated, yet reach significant values to slow down organelle motion or even limit their displacement by springing them back towards their original position. The cytoplasm may also be itself organized in time and space, being for example stiffer or more fluid at certain locations or during particular cell cycle phases. Thus, cytoplasm mechanics may be viewed as a labile module that contributes to organize cells. We here review emerging methods, mechanisms, and concepts to study cytoplasm mechanical properties and their function in organelle positioning, cellular organization and division.

Two-fluid dynamics and micron-thin boundary layers shape cytoplasmic flows in early Drosophila embryos

Cytoplasmic flows are widely emerging as key functional players in development. In early Drosophila embryos, flows drive the spreading of nuclei across the embryo. Here, we combine hydrodynamic modeling with quantitative imaging to develop a two-fluid model that features an active actomyosin gel and a passive viscous cytosol. Gel contractility is controlled by the cell cycle oscillator, the two fluids being coupled by friction. In addition to recapitulating experimental flow patterns, our model explains observations that remained elusive and makes a series of predictions. First, the model captures the vorticity of cytosolic flows, which highlights deviations from Stokes' flow that were observed experimentally but remained unexplained. Second, the model reveals strong differences in the gel and cytosol motion. In particular, a micron-sized boundary layer is predicted close to the cortex, where the gel slides tangentially while the cytosolic flow cannot slip. Third, the model unveils a mechanism that stabilizes the spreading of nuclei with respect to perturbations of their initial positions. This self-correcting mechanism is argued to be functionally important for proper nuclear spreading. Fourth, we use our model to analyze the effects of flows on the transport of the morphogen Bicoid and the establishment of its gradients. Finally, the model predicts that the flow strength should be reduced if the shape of the domain is more round, which is experimentally confirmed in Drosophila mutants. Thus, our two-fluid model explains flows and nuclear positioning in early Drosophila, while making predictions that suggest novel future experiments.

Length limitation of astral microtubules orients cell divisions in murine intestinal crypts

Planar spindle orientation is critical for epithelial tissue organization and is generally instructed by the long cell-shape axis or cortical polarity domains. We introduced mouse intestinal organoids in order to study spindle orientation in a monolayered mammalian epithelium. Although spindles were planar, mitotic cells remained elongated along the apico-basal (A-B) axis, and polarity complexes were segregated to basal poles, so that spindles oriented in an unconventional manner, orthogonal to both polarity and geometric cues. Using high-resolution 3D imaging, simulations, and cell-shape and cytoskeleton manipulations, we show that planar divisions resulted from a length limitation in astral microtubules (MTs) which precludes them from interacting with basal polarity, and orient spindles from the local geometry of apical domains. Accordingly, lengthening MTs affected spindle planarity, cell positioning, and crypt arrangement. We conclude that MT length regulation may serve as a key mechanism for spindles to sense local cell shapes and tissue forces to preserve mammalian epithelial architecture.

A fine balance among key biophysical factors is required for recovery of bipolar mitotic spindle from monopolar and multipolar abnormalities

During mitosis, equal partitioning of chromosomes into two daughter cells requires assembly of a bipolar mitotic spindle. Because the spindle poles are each organized by a centrosome in animal cells, centrosome defects can lead to monopolar or multipolar spindles. However, the cell can effectively recover the bipolar spindle by separating the centrosomes in monopolar spindles and clustering them in multipolar spindles. To interrogate how a cell can separate and cluster centrosomes as needed to form a bipolar spindle, we developed a biophysical model, based on experimental data, which uses effective potential energies to describe key mechanical forces driving centrosome movements during spindle assembly. Our model identified general biophysical factors crucial for robust bipolarization of spindles that start as monopolar or multipolar. These factors include appropriate force fluctuation between centrosomes, balance between repulsive and attractive forces between centrosomes, exclusion of the centrosomes from the cell center, proper cell size and geometry, and a limited centrosome number. Consistently, we found experimentally that bipolar centrosome clustering is promoted as mitotic cell aspect ratio and volume decrease in tetraploid cancer cells. Our model provides mechanistic explanations for many more experimental phenomena and a useful theoretical framework for future studies of spindle assembly.

Yolk granule fusion and microtubule aster formation regulate cortical granule translocation and exocytosis in zebrafish oocytes

Dynamic reorganization of the cytoplasm is key to many core cellular processes, such as cell division, cell migration, and cell polarization. Cytoskeletal rearrangements are thought to constitute the main drivers of cytoplasmic flows and reorganization. In contrast, remarkably little is known about how dynamic changes in size and shape of cell organelles affect cytoplasmic organization. Here, we show that within the maturing zebrafish oocyte, the surface localization of exocytosis-competent cortical granules (Cgs) upon germinal vesicle breakdown (GVBD) is achieved by the combined activities of yolk granule (Yg) fusion and microtubule aster formation and translocation. We find that Cgs are moved towards the oocyte surface through radially outward cytoplasmic flows induced by Ygs fusing and compacting towards the oocyte center in response to GVBD. We further show that vesicles decorated with the small Rab GTPase Rab11, a master regulator of vesicular trafficking and exocytosis, accumulate together with Cgs at the oocyte surface. This accumulation is achieved by Rab11-positive vesicles being transported by acentrosomal microtubule asters, the formation of which is induced by the release of CyclinB/Cdk1 upon GVBD, and which display a net movement towards the oocyte surface by preferentially binding to the oocyte actin cortex. We finally demonstrate that the decoration of Cgs by Rab11 at the oocyte surface is needed for Cg exocytosis and subsequent chorion elevation, a process central in egg activation. Collectively, these findings unravel a yet unrecognized role of organelle fusion, functioning together with cytoskeletal rearrangements, in orchestrating cytoplasmic organization during oocyte maturation.

Reliable and robust control of nucleus centering is contingent on nonequilibrium force patterns

Cell centers their division apparatus to ensure symmetric cell division, a challenging task when the governing dynamics is stochastic. Using fission yeast, we show that the patterning of nonequilibrium polymerization forces of microtubule (MT) bundles controls the precise localization of spindle pole body (SPB), and hence the division septum, at the onset of mitosis. We define two cellular objectives, reliability, the mean SPB position relative to the geometric center, and robustness, the variance of the SPB position, which are sensitive to genetic perturbations that change cell length, MT bundle number/orientation, and MT dynamics. We show that simultaneous control of reliability and robustness is required to minimize septum positioning error achieved by the wild type (WT). A stochastic model for the MT-based nucleus centering, with parameters measured directly or estimated using Bayesian inference, recapitulates the maximum fidelity of WT. Using this, we perform a sensitivity analysis of the parameters that control nuclear centering.

Two-fluid dynamics and micron-thin boundary layers shape cytoplasmic flows in early Drosophila embryos

Cytoplasmic flows are widely emerging as key functional players in development. In early Drosophila embryos, flows drive the spreading of nuclei across the embryo. Here, we combine hydrodynamic modeling with quantitative imaging to develop a two-fluid model that features an active actomyosin gel and a passive viscous cytosol. Gel contractility is controlled by the cell cycle oscillator, the two fluids being coupled by friction. In addition to recapitulating experimental flow patterns, our model explains observations that remained elusive, and makes a series of new predictions. First, the model captures the vorticity of cytosolic flows, which highlights deviations from Stokes' flow that were observed experimentally but remained unexplained. Second, the model reveals strong differences in the gel and cytosol motion. In particular, a micron-sized boundary layer is predicted close to the cortex, where the gel slides tangentially whilst the cytosolic flow cannot slip. Third, the model unveils a mechanism that stabilizes the spreading of nuclei with respect to perturbations of their initial positions. This self-correcting mechanism is argued to be functionally important for proper nuclear spreading. Fourth, we use our model to analyze the effects of flows on the transport of the morphogen Bicoid, and the establishment of its gradients. Finally, the model predicts that the flow strength should be reduced if the shape of the domain is more round, which is experimentally confirmed in Drosophila mutants. Thus, our two-fluid model explains flows and nuclear positioning in early Drosophila, while making predictions that suggest novel future experiments.

Dynamic microtubules slow down during their shrinkage phase

Microtubules are dynamic polymers that undergo stochastic transitions between growing and shrinking phases. The structural and chemical properties of these phases remain poorly understood. The transition from growth to shrinkage, termed catastrophe, is not a first-order reaction but rather a multistep process whose frequency increases with the growth time: the microtubule ages as the older microtubule tip becomes more unstable. Aging shows that the growing phase is not a single state but comprises several substates of increasing instability. To investigate whether the shrinking phase is also multistate, we characterized the kinetics of microtubule shrinkage following catastrophe using an in vitro reconstitution assay with purified tubulins. We found that the shrinkage speed is highly variable across microtubules and that the shrinkage speed of individual microtubules slows down over time by as much as several fold. The shrinkage slowdown was observed in both fluorescently labeled and unlabeled microtubules as well as in microtubules polymerized from tubulin purified from different species, suggesting that the shrinkage slowdown is a general property of microtubules. These results indicate that microtubule shrinkage, like catastrophe, is time dependent and that the shrinking microtubule tip passes through a succession of states of increasing stability. We hypothesize that the shrinkage slowdown is due to destabilizing events that took place during growth, which led to multistep catastrophe. This suggests that the aging associated with growth is also manifested during shrinkage, with the older, more unstable growing tip being associated with a faster depolymerizing shrinking tip.

ARK2 stabilizes the plus-end of microtubules and promotes microtubule bundling in Arabidopsis

Microtubule dynamics and organization are important for plant cell morphogenesis and development. The microtubule-based motor protein kinesins are mainly responsible for the transport of some organelles and vesicles, although several have also been shown to regulate microtubule organization. The ARMADILLO REPEAT KINESIN (ARK) family is a plant-specific motor protein subfamily that consists of three members (ARK1, ARK2, and ARK3) in Arabidopsis thaliana. ARK2 has been shown to participate in root epidermal cell morphogenesis. However, whether and how ARK2 associates with microtubules needs further elucidation. Here, we demonstrated that ARK2 co-localizes with microtubules and facilitates microtubule bundling in vitro and in vivo. Pharmacological assays and microtubule dynamics analyses indicated that ARK2 stabilizes cortical microtubules. Live-cell imaging revealed that ARK2 moves along cortical microtubules in a processive mode and localizes both at the plus-end and the sidewall of microtubules. ARK2 therefore tracks and stabilizes the growing plus-ends of microtubules, which facilitates the formation of parallel microtubule bundles.

Quantification of Microtubule Stutters: Dynamic Instability Behaviors that are Strongly Associated with Catastrophe

Microtubules (MTs) are cytoskeletal fibers that undergo dynamic instability (DI), a remarkable process involving phases of growth and shortening separated by stochastic transitions called catastrophe and rescue. Dissecting DI mechanism(s) requires first characterizing and quantifying these dynamics, a subjective process that often ignores complexity in MT behavior. We present a Statistical Tool for Automated Dynamic Instability Analysis (STADIA) that identifies and quantifies not only growth and shortening, but also a category of intermediate behaviors that we term “stutters.” During stutters, the rate of MT length change tends to be smaller in magnitude than during typical growth or shortening phases. Quantifying stutters and other behaviors with STADIA demonstrates that stutters precede most catastrophes in our in vitro experiments and dimer-scale MT simulations, suggesting that stutters are mechanistically involved in catastrophes. Related to this idea, we show that the anticatastrophe factor CLASP2γ works by promoting the return of stuttering MTs to growth. STADIA enables more comprehensive and data-driven analysis of MT dynamics compared with previous methods. The treatment of stutters as distinct and quantifiable DI behaviors provides new opportunities for analyzing mechanisms of MT dynamics and their regulation by binding proteins.

Spatial and Temporal Scaling of Microtubules and Mitotic Spindles

During cell division, the mitotic spindle, a macromolecular structure primarily comprised of microtubules, drives chromosome alignment and partitioning between daughter cells. Mitotic spindles can sense cellular dimensions in order to adapt their length and mass to cell size. This scaling capacity is particularly remarkable during early embryo cleavage when cells divide rapidly in the absence of cell growth, thus leading to a reduction of cell volume at each division. Although mitotic spindle size scaling can occur over an order of magnitude in early embryos, in many species the duration of mitosis is relatively short, constant throughout early development and independent of cell size. Therefore, a key challenge for cells during embryo cleavage is not only to assemble a spindle of proper size, but also to do it in an appropriate time window which is compatible with embryo development. How spatial and temporal scaling of the mitotic spindle is achieved and coordinated with the duration of mitosis remains elusive. In this review, we will focus on the mechanisms that support mitotic spindle spatial and temporal scaling over a wide range of cell sizes and cellular contexts. We will present current models and propose alternative mechanisms allowing cells to spatially and temporally coordinate microtubule and mitotic spindle assembly.

Self-organized optimal packing of kinesin-5-driven microtubule asters scales with cell size

Radial microtubule (MT) arrays or asters determine cell geometry in animal cells. Multiple asters interacting with motors, such as those in syncytia, form intracellular patterns, but the mechanical principles behind this are not clear. Here, we report that oocytes of the marine ascidian Phallusia mammillata treated with the drug BI-D1870 spontaneously form cytoplasmic MT asters, or cytasters. These asters form steady state segregation patterns in a shell just under the membrane. Cytaster centers tessellate the oocyte cytoplasm, that is divide it into polygonal structures, dominated by hexagons, in a kinesin-5-dependent manner, while inter-aster MTs form 'mini-spindles'. A computational model of multiple asters interacting with kinesin-5 can reproduce both tessellation patterns and mini-spindles in a manner specific to the number of MTs per aster, MT lengths and kinesin-5 density. Simulations predict that the hexagonal tessellation patterns scale with increasing cell size, when the packing fraction of asters in cells is ∼1.6. This self-organized in vivo tessellation by cytasters is comparable to the 'circle packing problem', suggesting that there is an intrinsic mechanical pattern-forming module that is potentially relevant to understanding the role of collective mechanics of cytoskeletal elements in embryogenesis. This article has an associated First Person interview with the first author of the paper.

Nucleus-Cytoskeleton Crosstalk During Mitotic Entry

In preparation for mitosis, cells undergo extensive reorganization of the cytoskeleton and nucleus, so that chromosomes can be efficiently segregated into two daughter cells. Coordination of these cytoskeletal and nuclear events occurs through biochemical regulatory pathways, orchestrated by Cyclin-CDK activity. However, recent studies provide evidence that physical forces are also involved in the early steps of spindle assembly. Here, we will review how the crosstalk of physical forces and biochemical signals coordinates nuclear and cytoplasmic events during the G2-M transition, to ensure efficient spindle assembly and faithful chromosome segregation.

Collective dynein transport of the nucleus by pulling on astral microtubules during Saccharomyces cerevisiae mitosis

Positioning the nucleus at the bud neck during Saccharomyces cerevisiae mitosis involves pulling forces of cytoplasmic dynein localized in the daughter cell. Although genetic analysis has revealed a complex network positioning the nucleus, quantification of the forces acting on the nucleus and the number of dyneins driving the process has remained difficult. To better understand the collective forces involved in nuclear positioning, we compare a model of dyneins-driven microtubule (MT) pulling, MT pushing, and cytoplasmic drag to experiments. During S. cerevisiae mitosis, MTs interacting with the cortex nucleated by the daughter spindle pole body (SPB) (SPB-D) are longer than the mother SPB (SPB-M), increasing further during spindle elongation in anaphase. Interphasic SPB mobility is effectively diffusive, while the mitotic mobility is directed. By optimizing a computational model of the mobility of the nucleus due to diffusion and MTs pushing at the cell membrane to experiment, we estimate the viscosity governing the drag force on nuclei during positioning. A force balance model of mitotic SPB mobility compared to experimental mobility suggests that even one or two dynein dimers are sufficient to move the nucleus in the bud neck. Using stochastic computer simulations of a budding cell, we find that punctate dynein localization can generate sufficient force to reel in the nucleus to the bud neck. Compared to uniform motor localization, puncta involve fewer motors suggesting a functional role for motor clustering. Stochastic simulations also suggest that a higher number of force generators than predicted by force balance may be required to ensure the robustness of spindle positioning.

Spindle scaling mechanisms

The mitotic spindle robustly scales with cell size in a plethora of different organisms. During development and throughout evolution, the spindle adjusts to cell size in metazoans and yeast in order to ensure faithful chromosome separation. Spindle adjustment to cell size occurs by the scaling of spindle length, spindle shape and the velocity of spindle assembly and elongation. Different mechanisms, depending on spindle structure and organism, account for these scaling relationships. The limited availability of critical spindle components, protein gradients, sequestration of spindle components, or post-translational modification and differential expression levels have been implicated in the regulation of spindle length and the spindle assembly/elongation velocity in a cell size-dependent manner. In this review, we will discuss the phenomenon and mechanisms of spindle length, spindle shape and spindle elongation velocity scaling with cell size.

Cytoplasm's Got Moves

Cytoplasm is a gel-like crowded environment composed of various macromolecules, organelles, cytoskeletal networks, and cytosol. The structure of the cytoplasm is highly organized and heterogeneous due to the crowding of its constituents and their effective compartmentalization. In such an environment, the diffusive dynamics of the molecules are restricted, an effect that is further amplified by clustering and anchoring of molecules. Despite the crowded nature of the cytoplasm at the microscopic scale, large-scale reorganization of the cytoplasm is essential for important cellular functions, such as cell division and polarization. How such mesoscale reorganization of the cytoplasm is achieved, especially for large cells such as oocytes or syncytial tissues that can span hundreds of micrometers in size, is only beginning to be understood. In this review, we will discuss recent advances in elucidating the molecular, cellular, and biophysical mechanisms by which the cytoskeleton drives cytoplasmic reorganization across different scales, structures, and species.

Destabilization of Long Astral Microtubules via Cdk1-Dependent Removal of GTSE1 from Their Plus Ends Facilitates Prometaphase Spindle Orientation

The precise regulation of microtubule dynamics over time and space in dividing cells is critical for several mitotic mechanisms that ultimately enable cell proliferation, tissue organization, and development. Astral microtubules, which extend from the centrosome toward the cell cortex, must be present for the mitotic spindle to properly orient, as well as for the faithful execution of anaphase and cytokinesis. However, little is understood about how the dynamic properties of astral microtubules are regulated spatiotemporally, or the contribution of astral microtubule dynamics to spindle positioning. The mitotic regulator Cdk1-CyclinB promotes destabilization of centrosomal microtubules and increased microtubule dynamics as cells enter mitosis, but how Cdk1 activity modulates astral microtubule stability, and whether it impacts spindle positioning, is unknown. Here, we uncover a mechanism revealing that Cdk1 destabilizes astral microtubules in prometaphase and thereby influences spindle reorientation. Phosphorylation of the EB1-dependent microtubule plus-end tracking protein GTSE1 by Cdk1 in early mitosis abolishes its interaction with EB1 and recruitment to microtubule plus ends. Loss of Cdk1 activity, or mutation of phosphorylation sites in GTSE1, induces recruitment of GTSE1 to growing microtubule plus ends in mitosis. This decreases the catastrophe frequency of astral microtubules and causes an increase in the number of long astral microtubules reaching the cell cortex, which restrains the ability of cells to reorient spindles along the long cellular axis in early mitosis. Astral microtubules thus must not only be present but also dynamic to allow the spindle to reorient, a state assisted by selective destabilization of long astral microtubules via Cdk1.

Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation require a threshold density of both cortical dyneins and coupling kinesins, while the onset is diffusion-limited with relation to the cortical dynein mobility. The coordinated rotational motion emerges due to the resolution of a 'tug-of-war' of multiple cortical dynein motors bound to MTs of the same aster by 'noise' in the form of MT dynamic instability. This transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests that biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in the presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to the particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

Collective effects of XMAP215, EB1, CLASP2, and MCAK lead to robust microtubule treadmilling

Treadmilling is a complex behavior of active polymers characterized by polymerization at one polymer end and simultaneous depolymerization at the other end. Treadmilling is an essential feature of cytoskeletal filaments driving actin-based cell motility, bacterial cell division and transport, and reorganization of microtubule arrays in plants. Although microtubule treadmilling occurs in many cellular contexts, how cells coordinate growth at microtubule plus ends and shrinkage at microtubule minus ends to achieve treadmilling is not understood. Here, we employ predictive computational modeling and a multiprotein in vitro assay to reconstitute cellular-like microtubule treadmilling. Our work provides a deeper understanding of how active polymer systems can be tuned to give rise to robust yet dynamic cytoskeletal architectures.

Microtubule network remodeling is essential for fundamental cellular processes including cell division, differentiation, and motility. Microtubules are active biological polymers whose ends stochastically and independently switch between phases of growth and shrinkage. Microtubule treadmilling, in which the microtubule plus end grows while the minus end shrinks, is observed in cells; however, the underlying mechanisms are not known. Here, we use a combination of computational and in vitro reconstitution approaches to determine the conditions leading to robust microtubule treadmilling. We find that microtubules polymerized from tubulin alone can treadmill, albeit with opposite directionality and order-of-magnitude slower rates than observed in cells. We then employ computational simulations to predict that the combinatory effects of four microtubule-associated proteins (MAPs), namely EB1, XMAP215, CLASP2, and MCAK, can promote fast and sustained plus-end-leading treadmilling. Finally, we experimentally confirm the predictions of our computational model using a multi-MAP, in vitro microtubule dynamics assay to reconstitute robust plus-end-leading treadmilling, consistent with observations in cells. Our results demonstrate how microtubule dynamics can be modulated to achieve a dynamic balance between assembly and disassembly at opposite polymer ends, resulting in treadmilling over long periods of time. Overall, we show how the collective effects of multiple components give rise to complex microtubule behavior that may be used for global network remodeling in cells.

Spatio-temporal correlations between catastrophe events in a microtubule bundle: a computational study

We explore correlations between dynamics of different microtubules in a bundle, via numerical simulations, using a one-dimensional stochastic model of a microtubule. The guanosine triphosphate (GTP)-bound tubulins undergo diffusion-limited binding to the tip. Random hydrolysis events take place along the microtubule and converts the bound GTP in tubulin to guanosine diphosphate (GDP). The microtubule starts depolymerising when the monomer at the tip becomes GDP-bound; in this case, detachment of GDP-tubulin ensues and continues until either GTP-bound tubulin is exposed or complete depolymerisation is achieved. In the latter case, the microtubule is defined to have undergone a "catastrophe". Our results show that, in general, the dynamics of growth and catastrophe in different microtubules are coupled to each other; the closer the microtubules are, the stronger the coupling. In particular, all microtubules grow slower, on average, when brought closer together. The reduction in growth velocity also leads to more frequent catastrophes. More dramatically, catastrophe events in the different microtubules forming a bundle are found to be correlated; a catastrophe event in one microtubule is more likely to be followed by a similar event in the same microtubule. This propensity of bunching disappears when the microtubules move farther apart.

Numerical Parameter Space Compression and Its Application to Biophysical Models

Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e., are sensitive to) only a subset of those parameters. This phenomenon is due to parameter space compression (PSC), in which a subset of parameters emerges as "stiff" as a function of time or space. PSC has only been used to explain analytically solvable physics models. We have generalized this result by developing a numerical approach to PSC that can be applied to any computational model. We validated our method against analytically solvable models of a random walk with drift and protein production and degradation. We then applied our method to a simple computational model of microtubule dynamic instability. We propose that numerical PSC has the potential to identify the low-dimensional structure of many computational models in biophysics. The low-dimensional structure of a model is easier to interpret and identifies the mechanisms and experiments that best characterize the system.

Studying Tau-Microtubule Interaction Using Single-Molecule TIRF Microscopy

Microtubule architecture depends on a complex network of microtubule-associated proteins (MAPs) that act in concert to modulate microtubule assembly/disassembly and spatial arrangement. In vitro reconstitution of cytoskeleton dynamics coupled to single-molecule fluorescence assays has opened new perspectives to quantify the interaction of MAPs with microtubules. Here, we present a Total Internal Reflection Fluorescence (TIRF) microscopy-based assay enabling the characterization of Tau interaction with dynamic microtubules at the single-molecule level. We describe protein sample preparation in flow cells, single-molecule acquisitions by TIRF microscopy, and quantitative analysis of Tau oligomerization states and dwell time on microtubules.

Electron tomography reveals aspects of spindle structure important for mechanical stability at metaphase

Metaphase spindles exert pole-directed forces on still-connected sister kinetochores. The spindle must counter these forces with extensive forces to prevent spindle collapse. In small spindles, kinetochore microtubules (KMTs) connect directly with the poles, and countering forces are supplied either by interdigitating MTs that form interpolar bundles or by astral MTs connected to the cell cortex. In bigger spindles, particularly those without structured poles, the origin of extensive forces is less obvious. We have used electron tomography of well-preserved metaphase cells to obtain structural evidence about interactions among different classes of MTs in metaphase spindles from Chlamydomonas rheinhardti and two strains of cultured mammalian cells. In all these spindles, KMTs approach close to and cross-bridge with the minus ends of non-KMTs, which form a framework that interdigitates near the spindle equator. Although this structure is not pole-connected, its organization suggests that it can support kinetochore tension. Analogous arrangements of MTs have been seen in even bigger spindles, such as metaphase spindles in Haemanthus endosperm and frog egg extracts. We present and discuss a hypothesis that rationalizes changes in spindle design with spindle size based on the negative exponential distribution of MT lengths in dynamically unstable populations of tubulin polymers.

Behaviors of individual microtubules and microtubule populations relative to critical concentrations: dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis

The concept of critical concentration (CC) is central to understanding the behavior of microtubules (MTs) and other cytoskeletal polymers. Traditionally, these polymers are understood to have one CC, measured in multiple ways and assumed to be the subunit concentration necessary for polymer assembly. However, this framework does not incorporate dynamic instability (DI), and there is work indicating that MTs have two CCs. We use our previously established simulations to confirm that MTs have (at least) two experimentally relevant CCs and to clarify the behavior of individuals and populations relative to the CCs. At free subunit concentrations above the lower CC (CC_Elongation), growth phases of individual filaments can occur transiently; above the higher CC (CC_NetAssembly), the population’s polymer mass will increase persistently. Our results demonstrate that most experimental CC measurements correspond to CC_NetAssembly, meaning that “typical” DI occurs below the concentration traditionally considered necessary for polymer assembly. We report that [free tubulin] at steady state does not equal CC_NetAssembly, but instead approaches CC_NetAssembly asymptotically as [total tubulin] increases, and depends on the number of stable MT nucleation sites. We show that the degree of separation between CC_Elongation and CC_NetAssembly depends on the rate of nucleotide hydrolysis. This clarified framework helps explain and unify many experimental observations.

Relationship between dynamic instability of individual microtubules and flux of subunits into and out of polymer

Behaviors of dynamic polymers such as microtubules and actin are frequently assessed at one or both of the following scales: (a) net assembly or disassembly of bulk polymer, (b) growth and shortening of individual filaments. Previous work has derived various forms of an equation to relate the rate of change in bulk polymer mass (i.e., flux of subunits into and out of polymer, often abbreviated as "J") to individual filament behaviors. However, these versions of the "J equation" differ in the variables used to quantify individual filament behavior, which correspond to different experimental approaches. For example, some variants of the J equation use dynamic instability parameters, obtained by following particular individual filaments for long periods of time. Another form of the equation uses measurements from many individuals followed over short time steps. We use a combination of derivations and computer simulations that mimic experiments to (a) relate the various forms of the J equation to each other, (b) determine conditions under which these J equation forms are and are not equivalent, and (c) identify aspects of the measurements that can affect the accuracy of each form of the J equation. Improved understanding of the J equation and its connections to experimentally measurable quantities will contribute to efforts to build a multiscale understanding of steady-state polymer behavior.

Augmin accumulation on long-lived microtubules drives amplification and kinetochore-directed growth

Vertebrate cells assemble mitotic spindles through multiple pathways. It is shown that Augmin-dependent, noncentrosomal nucleation generates the vast majority of microtubules in metaphase spindles. This results in a strong directional bias of microtubule growth toward individual kinetochores.

Dividing cells reorganize their microtubule cytoskeleton into a bipolar spindle, which moves one set of sister chromatids to each nascent daughter cell. Early spindle assembly models postulated that spindle pole–derived microtubules search the cytoplasmic space until they randomly encounter a kinetochore to form a stable attachment. More recent work uncovered several additional, centrosome-independent microtubule generation pathways, but the contributions of each pathway to spindle assembly have remained unclear. Here, we combined live microscopy and mathematical modeling to show that most microtubules nucleate at noncentrosomal regions in dividing human cells. Using a live-cell probe that selectively labels aged microtubule lattices, we demonstrate that the distribution of growing microtubule plus ends can be almost entirely explained by Augmin-dependent amplification of long-lived microtubule lattices. By ultrafast 3D lattice light-sheet microscopy, we observed that this mechanism results in a strong directional bias of microtubule growth toward individual kinetochores. Our systematic quantification of spindle dynamics reveals highly coordinated microtubule growth during kinetochore fiber assembly.

Spatiotemporal organization of branched microtubule networks

To understand how chromosomes are segregated, it is necessary to explain the precise spatiotemporal organization of microtubules (MTs) in the mitotic spindle. We use Xenopus egg extracts to study the nucleation and dynamics of MTs in branched networks, a process that is critical for spindle assembly. Surprisingly, new branched MTs preferentially originate near the minus-ends of pre-existing MTs. A sequential reaction model, consisting of deposition of nucleation sites on an existing MT, followed by rate-limiting nucleation of branches, reproduces the measured spatial profile of nucleation, the distribution of MT plus-ends and tubulin intensity. By regulating the availability of the branching effectors TPX2, augmin and γ-TuRC, combined with single-molecule observations, we show that first TPX2 is deposited on pre-existing MTs, followed by binding of augmin/γ-TuRC to result in the nucleation of branched MTs. In sum, regulating the localization and kinetics of nucleation effectors governs the architecture of branched MT networks.

The Physics of the Metaphase Spindle

The assembly of the mitotic spindle and the subsequent segregation of sister chromatids are based on the self-organized action of microtubule filaments, motor proteins, and other microtubule-associated proteins, which constitute the fundamental force-generating elements in the system. Many of the components in the spindle have been identified, but until recently it remained unclear how their collective behaviors resulted in such a robust bipolar structure. Here, we review the current understanding of the physics of the metaphase spindle that is only now starting to emerge.

Search and Capture Efficiency of Dynamic Microtubules for Centrosome Relocation during IS Formation

Upon contact with antigen-presenting cells, cytotoxic T lymphocytes (T cells) establish a highly organized contact zone denoted as the immunological synapse (IS). The formation of the IS implies relocation of the microtubule organizing center (MTOC) toward the contact zone, which necessitates a proper connection between the MTOC and the IS via dynamic microtubules (MTs). The efficiency of the MTs finding the IS within the relevant timescale is, however, still illusive. We investigate how MTs search the three-dimensional constrained cellular volume for the IS and bind upon encounter to dynein anchored at the IS cortex. The search efficiency is estimated by calculating the time required for the MTs to reach the dynein-enriched region of the IS. In this study, we develop simple mathematical and numerical models incorporating relevant components of a cell and propose an optimal search strategy. Using the mathematical model, we have quantified the average search time for a wide range of model parameters and proposed an optimized set of values leading to the minimal capture time. Our results show that search times are minimal when the IS formed at the nearest or at the farthest sites on the cell surface with respect to the perinuclear MTOC. The search time increases monotonically away from these two specific sites and is maximal at an intermediate position near the equator of the cell. We observed that search time strongly depends on the number of searching MTs and distance of the MTOC from the nuclear surface.

MTrack: Automated Detection, Tracking, and Analysis of Dynamic Microtubules

Microtubules are polar, dynamic filaments fundamental to many cellular processes. In vitro reconstitution approaches with purified tubulin are essential to elucidate different aspects of microtubule behavior. To date, deriving data from fluorescence microscopy images by manually creating and analyzing kymographs is still commonplace. Here, we present MTrack, implemented as a plug-in for the open-source platform Fiji, which automatically identifies and tracks dynamic microtubules with sub-pixel resolution using advanced objection recognition. MTrack provides automatic data interpretation yielding relevant parameters of microtubule dynamic instability together with population statistics. The application of our software produces unbiased and comparable quantitative datasets in a fully automated fashion. This helps the experimentalist to achieve higher reproducibility at higher throughput on a user-friendly platform. We use simulated data and real data to benchmark our algorithm and show that it reliably detects, tracks, and analyzes dynamic microtubules and achieves sub-pixel precision even at low signal-to-noise ratios.

Spastin is a dual-function enzyme that severs microtubules and promotes their regrowth to increase the number and mass of microtubules

The remodeling of the microtubule cytoskeleton underlies dynamic cellular processes, such as mitosis, ciliogenesis, and neuronal morphogenesis. An important class of microtubule remodelers comprises the severases-spastin, katanin, and fidgetin-which cut microtubules into shorter fragments. While severing activity might be expected to break down the microtubule cytoskeleton, inhibiting these enzymes in vivo actually decreases, rather increases, the number of microtubules, suggesting that severases have a nucleation-like activity. To resolve this paradox, we reconstituted Drosophila spastin in a dynamic microtubule assay and discovered that it is a dual-function enzyme. In addition to its ATP-dependent severing activity, spastin is an ATP-independent regulator of microtubule dynamics that slows shrinkage and increases rescue. We observed that spastin accumulates at shrinking ends; this increase in spastin concentration may underlie the increase in rescue frequency and the slowdown in shortening. The changes in microtubule dynamics promote microtubule regrowth so that severed microtubule fragments grow, leading to an increase in the number and mass of microtubules. A mathematical model shows that spastin's effect on microtubule dynamics is essential for this nucleation-like activity: spastin switches microtubules into a state where the net flux of tubulin onto each polymer is positive, leading to the observed exponential increase in microtubule mass. This increase in the microtubule mass accounts for spastin's in vivo phenotypes.

Aurora A Protein Kinase: To the Centrosome and Beyond

Accurate chromosome segregation requires the perfect spatiotemporal rearrangement of the cellular cytoskeleton. Isolated more than two decades ago from Drosophila, Aurora A is a widespread protein kinase that plays key roles during cell division. Numerous studies have described the localisation of Aurora A at centrosomes, the mitotic spindle, and, more recently, at mitotic centromeres. In this review, we will summarise the cytoskeletal rearrangements regulated by Aurora A during cell division. We will also discuss the recent discoveries showing that Aurora A also controls not only the dynamics of the cortical proteins but also regulates the centromeric proteins, revealing new roles for this kinase during cell division.

Emerging Insights into the Function of Kinesin-8 Proteins in Microtubule Length Regulation

Proper regulation of microtubules (MTs) is critical for the execution of diverse cellular processes, including mitotic spindle assembly and chromosome segregation. There are a multitude of cellular factors that regulate the dynamicity of MTs and play critical roles in mitosis. Members of the Kinesin-8 family of motor proteins act as MT-destabilizing factors to control MT length in a spatially and temporally regulated manner. In this review, we focus on recent advances in our understanding of the structure and function of the Kinesin-8 motor domain, and the emerging contributions of the C-terminal tail of Kinesin-8 proteins to regulate motor activity and localization.

microRNA-769 is downregulated in colorectal cancer and inhibits cancer progression by directly targeting cyclin-dependent kinase 1

BACKGROUND

In recent years, microRNAs (miRNAs) have been reported to be aberrantly expressed in colorectal cancer (CRC). The deregulation of miRNAs is implicated in the formation and progression of CRC, and participates in the regulation of a wide range of biological behaviors. Considering the crucial role of miRNAs in CRC, miRNAs are thought to have significant promise in the diagnosis and therapy of patients with this malignancy.

MATERIAL AND METHODS

Reverse transcription-quantitative polymerase chain reaction (RT-qPCR) was performed to detect miR-769 expression in CRC tissues and cell lines. MTT assay and flow cytometry analysis were used to determine the effects of miR-769 upregulation in CRC cell proliferation and apoptosis, respectively. The influence of miR-769 overexpression in CRC cell migration and invasion was evaluated through migration and invasion assays. Notably, the possible mechanisms underlying the action of miR-769 in CRC cells were explored.

RESULTS

In the present study, miR-769 was frequently found to be poorly expressed in CRC tissues and cell lines. Functional assays showed that recovery of miR-769 expression suppressed CRC cell proliferation, migration, and invasion, increased cell apoptosis in vitro, and inhibited tumor growth in vivo. Cyclin-dependent kinase 1 (CDK1) was the direct target of miR-769 in CRC cells. CDK1 was overexpressed in CRC tissue samples and negatively correlated with miR-769 expression. In addition, CDK1 inhibition imitated the tumor suppressor activity of miR-769 in CRC cells, and restoration of CDK1 expression partially abolished the tumor-suppressing roles of miR-769 in malignant CRC cells.

CONCLUSION

The results of this study demonstrated that miR-769 was downregulated in CRC and directly targeted CDK1 to be implicated in the regulation of CRC cell proliferation, apoptosis, migration and invasion. Thus, the miR-769/CDK1 axis might be an effective therapeutic target for treating patients with CRC.

Microtubule Dynamics Scale with Cell Size to Set Spindle Length and Assembly Timing

Successive cell divisions during embryonic cleavage create increasingly smaller cells, so intracellular structures must adapt accordingly. Mitotic spindle size correlates with cell size, but the mechanisms for this scaling remain unclear. Using live cell imaging, we analyzed spindle scaling during embryo cleavage in the nematode Caenorhabditis elegans and sea urchin Paracentrotus lividus. We reveal a common scaling mechanism, where the growth rate of spindle microtubules scales with cell volume, which explains spindle shortening. Spindle assembly timing is, however, constant throughout successive divisions. Analyses in silico suggest that controlling the microtubule growth rate is sufficient to scale spindle length and maintain a constant assembly timing. We tested our in silico predictions to demonstrate that modulating cell volume or microtubule growth rate in vivo induces a proportional spindle size change. Our results suggest that scalability of the microtubule growth rate when cell size varies adapts spindle length to cell volume.

Two-step interphase microtubule disassembly aids spindle morphogenesis

BACKGROUND

Entry into mitosis triggers profound changes in cell shape and cytoskeletal organisation. Here, by studying microtubule remodelling in human flat mitotic cells, we identify a two-step process of interphase microtubule disassembly.

RESULTS

First, a microtubule-stabilising protein, Ensconsin/MAP7, is inactivated in prophase as a consequence of its phosphorylation downstream of Cdk1/cyclin B. This leads to a reduction in interphase microtubule stability that may help to fuel the growth of centrosomally nucleated microtubules. The peripheral interphase microtubules that remain are then rapidly lost as the concentration of tubulin heterodimers falls following dissolution of the nuclear compartment boundary. Finally, we show that a failure to destabilise microtubules in prophase leads to the formation of microtubule clumps, which interfere with spindle assembly.

CONCLUSIONS

This analysis highlights the importance of the step-wise remodelling of the microtubule cytoskeleton and the significance of permeabilisation of the nuclear envelope in coordinating the changes in cellular organisation and biochemistry that accompany mitotic entry.

Understanding force-generating microtubule systems through in vitro reconstitution

Microtubules switch between growing and shrinking states, a feature known as dynamic instability. The biochemical parameters underlying dynamic instability are modulated by a wide variety of microtubule-associated proteins that enable the strict control of microtubule dynamics in cells. The forces generated by controlled growth and shrinkage of microtubules drive a large range of processes, including organelle positioning, mitotic spindle assembly, and chromosome segregation. In the past decade, our understanding of microtubule dynamics and microtubule force generation has progressed significantly. Here, we review the microtubule-intrinsic process of dynamic instability, the effect of external factors on this process, and how the resulting forces act on various biological systems. Recently, reconstitution-based approaches have strongly benefited from extensive biochemical and biophysical characterization of individual components that are involved in regulating or transmitting microtubule-driven forces. We will focus on the current state of reconstituting increasingly complex biological systems and provide new directions for future developments.

Tau-based fluorescent protein fusions to visualize microtubules

The ability to visualize cytoskeletal proteins and their dynamics in living cells has been critically important in advancing our understanding of numerous cellular processes, including actin- and microtubule (MT)-dependent phenomena such as cell motility, cell division, and mitosis. Here, we describe a novel set of fluorescent protein (FP) fusions designed specifically to visualize MTs in living systems using fluorescence microscopy. Each fusion contains a FP module linked in frame to a modified phospho-deficient version of the MT-binding domain of Tau (mTMBD). We found that expressed and purified constructs containing a single mTMBD decorated Xenopus egg extract spindles more homogenously than similar constructs containing the MT-binding domain of Ensconsin, suggesting that the binding affinity of mTMBD is minimally affected by localized signaling gradients generated during mitosis. Furthermore, MT dynamics were not grossly perturbed by the presence of Tau-based FP fusions. Interestingly, the addition of a second mTMBD to the opposite terminus of our construct caused dramatic changes to the spatial localization of probes within spindles. These results support the use of Tau-based FP fusions as minimally perturbing tools to accurately visualize MTs in living systems.

Geometric Asymmetry Induces Upper Limit of Mitotic Spindle Size

Proper organelle size is critical for many cell functions. However, how cells sense and control their organelle size remains elusive. Here, we develop a general model to study the size control of mitotic spindles by considering both extrinsic and intrinsic factors, such as the limited number of building blocks of the spindle, the interaction between the spindle and cell boundary, the DNA content, the forces generated by various molecular motors, and the dynamics of microtubules. We show that multiple pairs of chromatids, two centrosomes, and microtubules can self-assemble to form a mitotic spindle robustly. We also show that the boundary-sensing and volume-sensing mechanisms coexist in small cells, but both break down in large cells. Strikingly, we find that the upper limit of spindle length naturally arises from the geometric asymmetry of the spindle structure. Thus, our findings reveal, to our knowledge, a novel intrinsic mechanism that limits the organelle size.

Cytoskeleton Dynamics: Mind the Gap!

A new study presents a quantitative biophysical model of microtubule aster growth with autocatalytic microtubule nucleation. The model accounts for asters that grow indefinitely, even when their microtubules are unstable.

Inhibition of ectopic microtubule assembly by the kinesin-13 KLP-7 prevents chromosome segregation and cytokinesis defects in oocytes

In most species, oocytes lack centrosomes. Accurate meiotic spindle assembly and chromosome segregation - essential to prevent miscarriage or developmental defects - thus occur through atypical mechanisms that are not well characterized. Using quantitative in vitro and in vivo functional assays in the C. elegans oocyte, we provide novel evidence that the kinesin-13 KLP-7 promotes destabilization of the whole cellular microtubule network. By counteracting ectopic microtubule assembly and disorganization of the microtubule network, this function is strictly required for spindle organization, chromosome segregation and cytokinesis in meiotic cells. Strikingly, when centrosome activity was experimentally reduced, the absence of KLP-7 or the mammalian kinesin-13 protein MCAK (KIF2C) also resulted in ectopic microtubule asters during mitosis in C. elegans zygotes or HeLa cells, respectively. Our results highlight the general function of kinesin-13 microtubule depolymerases in preventing ectopic, spontaneous microtubule assembly when centrosome activity is defective or absent, which would otherwise lead to spindle microtubule disorganization and aneuploidy.

Theoretical model of mitotic spindle microtubule growth for FRAP curve interpretation

Background

Spindle FRAP curves depend on the kinetic parameters of microtubule polymerization and depolymerization. The empirical FRAP curve proposed earlier permits determination of only one such dynamic parameter, commonly called the "tubulin turnover". The aim of our study was to build a FRAP curve based on an already known kinetic model of microtubule growth.

Results

A numerical expression that describes the distribution of polymerizing and depolymerizing microtubule ends as a function of four kinetic parameters is presented. In addition, a theoretical FRAP curve for the metaphase spindle is constructed using previously published dynamic parameters.

Conclusion

The numerical expression we elaborated can replace the empirical FRAP curve described earlier for a spindle comprising fluorescently marked microtubules. The curve we generated fits well the experimental data.

Anaphase A: Disassembling Microtubules Move Chromosomes toward Spindle Poles

The separation of sister chromatids during anaphase is the culmination of mitosis and one of the most strikingly beautiful examples of cellular movement. It consists of two distinct processes: Anaphase A, the movement of chromosomes toward spindle poles via shortening of the connecting fibers, and anaphase B, separation of the two poles from one another via spindle elongation. I focus here on anaphase A chromosome-to-pole movement. The chapter begins by summarizing classical observations of chromosome movements, which support the current understanding of anaphase mechanisms. Live cell fluorescence microscopy studies showed that poleward chromosome movement is associated with disassembly of the kinetochore-attached microtubule fibers that link chromosomes to poles. Microtubule-marking techniques established that kinetochore-fiber disassembly often occurs through loss of tubulin subunits from the kinetochore-attached plus ends. In addition, kinetochore-fiber disassembly in many cells occurs partly through 'flux', where the microtubules flow continuously toward the poles and tubulin subunits are lost from minus ends. Molecular mechanistic models for how load-bearing attachments are maintained to disassembling microtubule ends, and how the forces are generated to drive these disassembly-coupled movements, are discussed.

Katanin Effects on Dynamics of Cortical Microtubules and Mitotic Arrays in Arabidopsis thaliana Revealed by Advanced Live-Cell Imaging

Katanin is the only microtubule severing protein identified in plants so far. Previous studies have documented its role in regulating cortical microtubule organization during cell growth and morphogenesis. Although, some cell division defects are reported in KATANIN mutants, it is not clear whether or how katanin activity may affect microtubule dynamics in interphase cells, as well as the progression of mitosis and cytokinesis and the orientation of cell division plane (CDP). For this reason, we characterized microtubule organization and dynamics in growing and dividing cotyledon cells of Arabidopsis ktn1-2 mutant devoid of KATANIN 1 activity. In interphase epidermal cells of ktn1-2 cortical microtubules exhibited aberrant and largely isotropic organization, reduced bundling and showed excessive branched microtubule formation. End-wise microtubule dynamics were not much affected, although a significantly slower rate of microtubule growth was measured in the ktn1-2 mutant where microtubule severing was completely abolished. KATANIN 1 depletion also brought about significant changes in preprophase microtubule band (PPB) organization and dynamics. In this case, many PPBs exhibited unisided organization and splayed appearance while in most cases they were broader than those of wild type cells. By recording PPB maturation, it was observed that PPBs in the mutant narrowed at a much slower pace compared to those in Col-0. The form of the mitotic spindle and the phragmoplast was not much affected in ktn1-2, however, the dynamics of both processes showed significant differences compared to wild type. In general, both mitosis and cytokinesis were considerably delayed in the mutant. Additionally, the mitotic spindle and the phragmoplast exhibited extensive rotational motions with the equatorial plane of the spindle being essentially uncoupled from the division plane set by the PPB. However, at the onset of its formation the phragmoplast undergoes rotational motion rectifying the expansion of the cell plate to match the original cell division plane. Conclusively, KATANIN 1 contributes to microtubule dynamics during interphase, regulates PPB formation and maturation and is involved in the positioning of the mitotic spindle and the phragmoplast.

Physical basis of large microtubule aster growth

Microtubule asters - radial arrays of microtubules organized by centrosomes - play a fundamental role in the spatial coordination of animal cells. The standard model of aster growth assumes a fixed number of microtubules originating from the centrosomes. However, aster morphology in this model does not scale with cell size, and we recently found evidence for non-centrosomal microtubule nucleation. Here, we combine autocatalytic nucleation and polymerization dynamics to develop a biophysical model of aster growth. Our model predicts that asters expand as traveling waves and recapitulates all major aspects of aster growth. With increasing nucleation rate, the model predicts an explosive transition from stationary to growing asters with a discontinuous jump of the aster velocity to a nonzero value. Experiments in frog egg extract confirm the main theoretical predictions. Our results suggest that asters observed in large fish and amphibian eggs are a meshwork of short, unstable microtubules maintained by autocatalytic nucleation and provide a paradigm for the assembly of robust and evolvable polymer networks.

DOI:http://dx.doi.org/10.7554/eLife.19145.001

Cells must carefully organize their contents in order to work effectively. Protein filaments called microtubules often play important roles in this organization, as well as giving structure to the cell. Many cells contain structures called asters that are formed of microtubules that radiate out from a central point (much like a star shape). Textbooks generally state that all microtubules in the aster grow outward from its center. If this was the case, the microtubules at the edge of large asters – such as those found in frog egg cells and other extremely large cells – would be spread relatively far apart from each other. However, even at the edges of large asters, the microtubules are quite densely packed.

In 2014, a group of researchers proposed that new microtubules could form throughout the aster instead of all originating from the center. This model had not been tested; it was also unclear under what conditions an aster would be able to grow to fill a large cell.

Ishihara et al. – including some of the researchers involved in the 2014 work – have now developed a mathematical theory of aster growth that is based on the assumption that microtubules stimulate the generation of new microtubules. The theory reproduces the key features seen during the growth of asters in large cells, and predicts that the asters may stay at a constant size or grow continuously. The condition required for the aster to grow is simple: each microtubule in it has to trigger the generation of at least one new microtubule during its lifetime. Ishihara et al. have named this process “collective growth”.

Experiments performed using microtubules taken from crushed frog eggs and assembled under a cover slip provided further evidence that asters grow via a collective growth process. Future studies could now investigate whether collective growth also underlies the formation of other cellular structures.

DOI:http://dx.doi.org/10.7554/eLife.19145.002

A Motor-Gradient and Clustering Model of the Centripetal Motility of MTOCs in Meiosis I of Mouse Oocytes

Asters nucleated by Microtubule (MT) organizing centers (MTOCs) converge on chromosomes during spindle assembly in mouse oocytes undergoing meiosis I. Time-lapse imaging suggests that this centripetal motion is driven by a biased 'search-and-capture' mechanism. Here, we develop a model of a random walk in a drift field to test the nature of the bias and the spatio-temporal dynamics of the search process. The model is used to optimize the spatial field of drift in simulations, by comparison to experimental motility statistics. In a second step, this optimized gradient is used to determine the location of immobilized dynein motors and MT polymerization parameters, since these are hypothesized to generate the gradient of forces needed to move MTOCs. We compare these scenarios to self-organized mechanisms by which asters have been hypothesized to find the cell-center- MT pushing at the cell-boundary and clustering motor complexes. By minimizing the error between simulation outputs and experiments, we find a model of "pulling" by a gradient of dynein motors alone can drive the centripetal motility. Interestingly, models of passive MT based "pushing" at the cortex, clustering by cross-linking motors and MT-dynamic instability gradients alone, by themselves do not result in the observed motility. The model predicts the sensitivity of the results to motor density and stall force, but not MTs per aster. A hybrid model combining a chromatin-centered immobilized dynein gradient, diffusible minus-end directed clustering motors and pushing at the cell cortex, is required to comprehensively explain the available data. The model makes experimentally testable predictions of a spatial bias and self-organized mechanisms by which MT asters can find the center of a large cell.

Regulation of Microtubule Growth and Catastrophe: Unifying Theory and Experiment

Recent studies have found that microtubule-associated proteins (MAPs) can regulate the dynamical properties of microtubules in unexpected ways. For most MAPs, there is an inverse relationship between their effects on the speed of growth and the frequency of catastrophe, the conversion of a growing microtubule to a shrinking one. Such a negative correlation is predicted by the standard GTP-cap model, which posits that catastrophe is due to loss of a stabilizing cap of GTP-tubulin at the end of a growing microtubule. However, many other MAPs, notably Kinesin-4 and combinations of EB1 with XMAP215, contradict this general rule. In this review, we show that a more nuanced, but still simple, GTP-cap model, can account for the diverse regulatory activities of MAPs.

The sequential activation of the mitotic microtubule assembly pathways favors bipolar spindle formation

A combination of experimental data obtained in somatic cells and Xenopus egg extracts and modeling suggests a novel function for centrosome maturation that balances the activity of the mitotic microtubule assembly pathways favoring bipolar spindle formation.

Centrosome maturation is the process by which the duplicated centrosomes recruit pericentriolar components and increase their microtubule nucleation activity before mitosis. The role of this process in cells entering mitosis has been mostly related to the separation of the duplicated centrosomes and thereby to the assembly of a bipolar spindle. However, spindles can form without centrosomes. In fact, all cells, whether they have centrosomes or not, rely on chromatin-driven microtubule assembly to form a spindle. To test whether the sequential activation of these microtubule assembly pathways, defined by centrosome maturation and nuclear envelope breakdown, plays any role in spindle assembly, we combined experiments in tissue culture cells and Xenopus laevis egg extracts with a mathematical model. We found that interfering with the sequential activation of the microtubule assembly pathways compromises bipolar spindle assembly in tissue culture cells but not in X. laevis egg extracts. Our data suggest a novel function for centrosome maturation that determines the contribution of the chromosomal microtubule assembly pathway and favors bipolar spindle formation in most animal cells in which tubulin is in limiting amounts.