Autocatalytic microtubule nucleation determines the size and mass of Xenopus laevis egg extract spindles

Neurons exploit stochastic growth to rapidly and economically build dense radially oriented dendritic arbors

Dendrites grow by stochastic branching, elongation, and retraction. A key question is whether such a mechanism is sufficient to form highly branched dendritic morphologies. Alternatively, are signals from other cells or is the topological hierarchy of the growing network necessary for dendrite geometry? To answer these questions, we developed a mean-field model in which branch dynamics is isotropic and homogenous (i.e., no extrinsic instruction) and depends only on the average lengths and densities of branches. Branching is modeled as density-dependent nucleation so there are no tree structures and no network topology. Despite its simplicity, the model predicted several key morphological properties of class IV Drosophila sensory dendrites, including the exponential distribution of branch lengths, the parabolic scaling between dendrite number and length densities, the tight spacing of the dendritic meshwork (which required minimal total branch length), and the radial orientation of branches. Stochastic growth also accelerated the overall expansion rate of the arbor. Therefore, stochastic dynamics is an economical and rapid space-filling mechanism for building dendritic arbors without external guidance or hierarchical branching mechanisms. Our model provides a general theoretical framework for understanding how macroscopic branching patterns emerge from microscopic dynamics.

Developmental Control of Cell Cycle and Signaling

In most species, the earliest stages of embryogenesis are characterized by rapid proliferation, which must be tightly controlled with other cellular processes across the large scale of the embryo. The study of this coordination has recently revealed new mechanisms of regulation of morphogenesis. Here, I discuss progress on how the integration of biochemical and mechanical signals leads to the proper positioning of cellular components, how signaling waves ensure the synchronization of the cell cycle, and how cell cycle transitions are properly timed. Similar concepts are emerging in the control of morphogenesis of other tissues, highlighting both common and unique features of early embryogenesis.

Robust cytoplasmic partitioning by solving an intrinsic cytoskeletal instability

Early development across vertebrates and insects critically relies on robustly reorganizing the cytoplasm of fertilized eggs into individualized cells. This intricate process is orchestrated by large microtubule structures that traverse the embryo, partitioning the cytoplasm into physically distinct and stable compartments. Despite the robustness of embryonic development, here we uncover an intrinsic instability in cytoplasmic partitioning driven by the microtubule cytoskeleton. We reveal that embryos circumvent this instability through two distinct mechanisms: either by matching the cell cycle duration to the time needed for the instability to unfold or by limiting microtubule nucleation. These regulatory mechanisms give rise to two possible strategies to fill the cytoplasm, which we experimentally demonstrate in zebrafish and Drosophila embryos, respectively. In zebrafish embryos, unstable microtubule waves fill the geometry of the entire embryo from the first division. Conversely, in Drosophila embryos, stable microtubule asters resulting from reduced microtubule nucleation gradually fill the cytoplasm throughout multiple divisions. Our results indicate that the temporal control of microtubule dynamics could have driven the evolutionary emergence of species-specific mechanisms for effective cytoplasmic organization. Furthermore, our study unveils a fundamental synergy between physical instabilities and biological clocks, uncovering universal strategies for rapid, robust, and efficient spatial ordering in biological systems.

Ultrasensitivity of microtubule severing due to damage repair

Microtubule-based cytoskeletal structures aid in cell motility, cell polarization, and intracellular transport. These functions require a coordinated effort of regulatory proteins which interact with microtubule cytoskeleton distinctively. In-vitro experiments have shown that free tubulin can repair nanoscale damages of microtubules created by severing proteins. Based on this observation, we theoretically analyze microtubule severing as a competition between the processes of damage spreading and tubulin-induced repair. We demonstrate that this model is in quantitative agreement with in-vitro experiments and predict the existence of a critical tubulin concentration above which severing becomes rare, fast, and sensitive to concentration of free tubulin. We show that this sensitivity leads to a dramatic increase in the dynamic range of steady-state microtubule lengths when the free tubulin concentration is varied, and microtubule lengths are controlled by severing. Our work demonstrates how synergy between tubulin and microtubule-associated proteins can bring about specific dynamical properties of microtubules.

Building on-chip cytoskeletal circuits via branched microtubule networks

Controllable platforms to engineer robust cytoskeletal scaffolds have the potential to create novel on-chip nanotechnologies. Inspired by axons, we combined the branching microtubule (MT) nucleation pathway with microfabrication to develop "cytoskeletal circuits." This active matter platform allows control over the adaptive self-organization of uniformly polarized MT arrays via geometric features of microstructures designed within a microfluidic confinement. We build and characterize basic elements, including turns and divisions, as well as complex regulatory elements, such as biased division and MT diodes, to construct various MT architectures on a chip. Our platform could be used in diverse applications, ranging from efficient on-chip molecular transport to mechanical nano-actuators. Further, cytoskeletal circuits can serve as a tool to study how the physical environment contributes to MT architecture in living cells.

Branched microtubule nucleation and dynein transport organize RanGTP asters in Xenopus laevis egg extract

Chromosome segregation relies on the correct assembly of a bipolar spindle. Spindle pole self-organization requires dynein-dependent microtubule (MT) transport along other MTs. However, during M-phase RanGTP triggers MT nucleation and branching generating polarized arrays with nonastral organization in which MT minus ends are linked to the sides of other MTs. This raises the question of how branched-MT nucleation and dynein-mediated transport cooperate to organize the spindle poles. Here, we used RanGTP-dependent MT aster formation in Xenopus laevis (X. laevis) egg extract to study the interplay between these two seemingly conflicting organizing principles. Using temporally controlled perturbations of MT nucleation and dynein activity, we found that branched MTs are not static but instead dynamically redistribute over time as poles self-organize. Our experimental data together with computer simulations suggest a model where dynein together with dynactin and NuMA directly pulls and move branched MT minus ends toward other MT minus ends.

Macromolecular condensation buffers intracellular water potential

Optimum protein function and biochemical activity critically depends on water availability because solvent thermodynamics drive protein folding and macromolecular interactions1. Reciprocally, macromolecules restrict the movement of 'structured' water molecules within their hydration layers, reducing the available 'free' bulk solvent and therefore the total thermodynamic potential energy of water, or water potential. Here, within concentrated macromolecular solutions such as the cytosol, we found that modest changes in temperature greatly affect the water potential, and are counteracted by opposing changes in osmotic strength. This duality of temperature and osmotic strength enables simple manipulations of solvent thermodynamics to prevent cell death after extreme cold or heat shock. Physiologically, cells must sustain their activity against fluctuating temperature, pressure and osmotic strength, which impact water availability within seconds. Yet, established mechanisms of water homeostasis act over much slower timescales2,3; we therefore postulated the existence of a rapid compensatory response. We find that this function is performed by water potential-driven changes in macromolecular assembly, particularly biomolecular condensation of intrinsically disordered proteins. The formation and dissolution of biomolecular condensates liberates and captures free water, respectively, quickly counteracting thermal or osmotic perturbations of water potential, which is consequently robustly buffered in the cytoplasm. Our results indicate that biomolecular condensation constitutes an intrinsic biophysical feedback response that rapidly compensates for intracellular osmotic and thermal fluctuations. We suggest that preserving water availability within the concentrated cytosol is an overlooked evolutionary driver of protein (dis)order and function.

Microtubule nucleation for spindle assembly: one molecule at a time

The cell orchestrates the dance of chromosome segregation with remarkable speed and fidelity. The mitotic spindle is built from scratch after interphase through microtubule (MT) nucleation, which is dependent on the γ-tubulin ring complex (γ-TuRC), the universal MT template. Although several MT nucleation pathways build the spindle framework, the question of when and how γ-TuRC is targeted to these nucleation sites in the spindle and subsequently activated remains an active area of investigation. Recent advances facilitated the discovery of new MT nucleation effectors and their mechanisms of action. In this review, we illuminate each spindle assembly pathway and subsequently consider how the pathways are merged to build a spindle.

Mechanisms underlying spindle assembly and robustness

The microtubule-based spindle orchestrates chromosome segregation during cell division. Following more than a century of study, many components and pathways contributing to spindle assembly have been described, but how the spindle robustly assembles remains incompletely understood. This process involves the self-organization of a large number of molecular parts - up to hundreds of thousands in vertebrate cells - whose local interactions give rise to a cellular-scale structure with emergent architecture, mechanics and function. In this Review, we discuss key concepts in our understanding of spindle assembly, focusing on recent advances and the new approaches that enabled them. We describe the pathways that generate the microtubule framework of the spindle by driving microtubule nucleation in a spatially controlled fashion and present recent insights regarding the organization of individual microtubules into structural modules. Finally, we discuss the emergent properties of the spindle that enable robust chromosome segregation.

Acentrosomal spindles assemble from branching microtubule nucleation near chromosomes in Xenopus laevis egg extract

Microtubules are generated at centrosomes, chromosomes, and within spindles during cell division. Whereas microtubule nucleation at the centrosome is well characterized, much remains unknown about where, when, and how microtubules are nucleated at chromosomes. To address these questions, we reconstitute microtubule nucleation from purified chromosomes in meiotic Xenopus egg extract and find that chromosomes alone can form spindles. We visualize microtubule nucleation near chromosomes using total internal reflection fluorescence microscopy to find that this occurs through branching microtubule nucleation. By inhibiting molecular motors, we find that the organization of the resultant polar branched networks is consistent with a theoretical model where the effectors for branching nucleation are released by chromosomes, forming a concentration gradient that spatially biases branching microtbule nucleation. In the presence of motors, these branched networks are ultimately organized into functional spindles, where the number of emergent spindle poles scales with the number of chromosomes and total chromatin area.

Structural basis of protein condensation on microtubules underlying branching microtubule nucleation

Targeting protein for Xklp2 (TPX2) is a key factor that stimulates branching microtubule nucleation during cell division. Upon binding to microtubules (MTs), TPX2 forms condensates via liquid-liquid phase separation, which facilitates recruitment of microtubule nucleation factors and tubulin. We report the structure of the TPX2 C-terminal minimal active domain (TPX2α5-α7) on the microtubule lattice determined by magic-angle-spinning NMR. We demonstrate that TPX2α5-α7 forms a co-condensate with soluble tubulin on microtubules and binds to MTs between two adjacent protofilaments and at the intersection of four tubulin heterodimers. These interactions stabilize the microtubules and promote the recruitment of tubulin. Our results reveal that TPX2α5-α7 is disordered in solution and adopts a folded structure on MTs, indicating that TPX2α5-α7 undergoes structural changes from unfolded to folded states upon binding to microtubules. The aromatic residues form dense interactions in the core, which stabilize folding of TPX2α5-α7 on microtubules. This work informs on how the phase-separated TPX2α5-α7 behaves on microtubules and represents an atomic-level structural characterization of a protein that is involved in a condensate on cytoskeletal filaments.

Augmin is a Ran-regulated spindle assembly factor

Mitotic spindles are composed of microtubules (MTs) that must nucleate at the right place and time. Ran regulates this process by directly controlling the release of spindle assembly factors (SAFs) from nucleocytoplasmic shuttle proteins importin-αβ and subsequently forms a biochemical gradient of SAFs localized around chromosomes. The majority of spindle MTs are generated by branching MT nucleation, which has been shown to require an eight-subunit protein complex known as augmin. InXenopus laevis, Ran can control branching through a canonical SAF, TPX2, which is non-essential in Drosophila melanogaster embryos and HeLa cells. Thus, how Ran regulates branching MT nucleation when TPX2 is not required remains unknown. Here, we use in vitro pulldowns and TIRF microscopy to show that augmin is a Ran-regulated SAF. We demonstrate that augmin directly interacts with both importin-α and importin-β through two nuclear localization sequences on the Haus8 subunit, which overlap with the MT binding site. Moreover, we show Ran controls localization of augmin to MTs in both Xenopus egg extract and in vitro. Our results demonstrate that RanGTP directly regulates augmin, which establishes a new way by which Ran controls branching MT nucleation and spindle assembly both in the absence and presence of TPX2.

Length Regulation Drives Self-Organization in Filament-Motor Mixtures

Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament clusters despite the absence of mechanical interactions between filaments. Even though the orientation of individual remains fixed, collective filament orientation emerges in the clusters, aligned orthogonal to their interfaces.

Morphological growth dynamics, mechanical stability, and active microtubule mechanics underlying spindle self-organization

The spindle is a dynamic intracellular structure self-organized from microtubules and microtubule-associated proteins. The spindle’s bipolar morphology is essential for the faithful segregation of chromosomes during cell division, and it is robustly maintained by multifaceted mechanisms. However, abnormally shaped spindles, such as multipolar spindles, can stochastically arise in a cell population and cause chromosome segregation errors. The physical basis of how microtubules fail in bipolarization and occasionally favor nonbipolar assembly is poorly understood. Here, using live fluorescence imaging and quantitative shape analysis in Xenopus egg extracts, we find that spindles of varied shape morphologies emerge through nonrandom, bistable self-organization paths, one leading to a bipolar and the other leading to a multipolar phenotype. The bistability defines the spindle’s unique morphological growth dynamics linked to each shape phenotype and can be promoted by a locally distorted microtubule flow that arises within premature structures. We also find that bipolar and multipolar spindles are stable at the steady-state in bulk but can infrequently switch between the two phenotypes. Our microneedle-based physical manipulation further demonstrates that a transient force perturbation applied near the assembled pole can trigger the phenotypic switching, revealing the mechanical plasticity of the spindle. Together with molecular perturbation of kinesin-5 and augmin, our data propose the physical and molecular bases underlying the emergence of spindle-shape variation, which influences chromosome segregation fidelity during cell division.

Dynamic instability of dendrite tips generates the highly branched morphologies of sensory neurons

The highly ramified arbors of neuronal dendrites provide the substrate for the high connectivity and computational power of the brain. Altered dendritic morphology is associated with neuronal diseases. Many molecules have been shown to play crucial roles in shaping and maintaining dendrite morphology. However, the underlying principles by which molecular interactions generate branched morphologies are not understood. To elucidate these principles, we visualized the growth of dendrites throughout larval development of Drosophila sensory neurons and found that the tips of dendrites undergo dynamic instability, transitioning rapidly and stochastically between growing, shrinking, and paused states. By incorporating these measured dynamics into an agent-based computational model, we showed that the complex and highly variable dendritic morphologies of these cells are a consequence of the stochastic dynamics of their dendrite tips. These principles may generalize to branching of other neuronal cell types, as well as to branching at the subcellular and tissue levels.

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-Organization of Cellular Units

The purpose of this review is to explore self-organizing mechanisms that pattern microtubules (MTs) and spatially organize animal cell cytoplasm, inspired by recent experiments in frog egg extract. We start by reviewing conceptual distinctions between self-organizing and templating mechanisms for subcellular organization. We then discuss self-organizing mechanisms that generate radial MT arrays and cell centers in the absence of centrosomes. These include autocatalytic MT nucleation, transport of minus ends, and nucleation from organelles such as melanosomes and Golgi vesicles that are also dynein cargoes. We then discuss mechanisms that partition the cytoplasm in syncytia, in which multiple nuclei share a common cytoplasm, starting with cytokinesis, when all metazoan cells are transiently syncytial. The cytoplasm of frog eggs is partitioned prior to cytokinesis by two self-organizing modules, protein regulator of cytokinesis 1 (PRC1)-kinesin family member 4A (KIF4A) and chromosome passenger complex (CPC)-KIF20A. Similar modules may partition longer-lasting syncytia, such as early Drosophila embryos. We end by discussing shared mechanisms and principles for the MT-based self-organization of cellular units.

Interaction of spindle assembly factor TPX2 with importins-α/β inhibits protein phase separation

The microtubule-based mitotic spindle is responsible for equally partitioning the genome during each cell division, and its assembly is executed via several microtubule nucleation pathways. Targeting Protein for XKlp2 (TPX2) stimulates the branching microtubule nucleation pathway, where new microtubules are nucleated from preexisting ones within mitotic or meiotic spindles. TPX2, like other spindle assembly factors, is sequestered by binding to nuclear importins-α/β until the onset of mitosis, yet the molecular nature of this regulation remains unclear. Here we demonstrate that TPX2 interacts with importins-α/β with nanomolar affinity in a 1:1:1 monodispersed trimer. We also identify a new nuclear localization sequence in TPX2 that contributes to its high-affinity interaction with importin-α. In addition, we establish that TPX2 interacts with importin-β via dispersed, weak interactions. We show that interactions of both importin-α and -β with TPX2 inhibit its ability to undergo phase separation, which was recently shown to enhance the kinetics of branching microtubule nucleation. In summary, our study informs how importins regulate TPX2 to facilitate spindle assembly, and provides novel insight into the functional regulation of protein phase separation.

The Xenopus spindle is as dense as the surrounding cytoplasm

The mitotic spindle is a self-organizing molecular machine, where hundreds of different molecules continuously interact to maintain a dynamic steady state. While our understanding of key molecular players in spindle assembly is significant, it is still largely unknown how the spindle's material properties emerge from molecular interactions. Here, we use correlative fluorescence imaging and label-free three-dimensional optical diffraction tomography (ODT) to measure the Xenopus spindle's mass density distribution. While the spindle has been commonly referred to as a denser phase of the cytoplasm, we find that it has the same density as its surrounding, which makes it neutrally buoyant. Molecular perturbations suggest that spindle mass density can be modulated by tuning microtubule nucleation and dynamics. Together, ODT provides direct, unbiased, and quantitative information of the spindle's emergent physical properties-essential to advance predictive frameworks of spindle assembly and function.

Confinement size determines the architecture of Ran-induced microtubule networks

The organization of microtubules (MTs) is critical for cells during interphase and mitosis. During mitotic spindle assembly, MTs are made and organized around chromosomes in a process regulated by RanGTP. The role of RanGTP has been explored in Xenopus egg extracts, which are not limited by a cell membrane. Here, we investigated whether cell-sized confinements affect the assembly of RanGTP-induced MT networks in Xenopus egg extracts. We used microfluidics to encapsulate extracts within monodisperse extract-in-oil droplets. Importantly, we find that the architecture of Ran-induced MT networks depends on the droplet diameter and the Ran concentration, and differs from structures formed in bulk extracts. Our results highlight that both MT nucleation and physical confinement play critical roles in determining the spatial organization of the MT cytoskeleton.

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.

Spatial variation of microtubule depolymerization in large asters

Microtubule plus-end depolymerization rate is a potentially important target of physiological regulation, but it has been challenging to measure, so its role in spatial organization is poorly understood. Here we apply a method for tracking plus ends based on time difference imaging to measure depolymerization rates in large interphase asters growing in Xenopus egg extract. We observed strong spatial regulation of depolymerization rates, which were higher in the aster interior compared with the periphery, and much less regulation of polymerization or catastrophe rates. We interpret these data in terms of a limiting component model, where aster growth results in lower levels of soluble tubulin and microtubule-associated proteins (MAPs) in the interior cytosol compared with that at the periphery. The steady-state polymer fraction of tubulin was ∼30%, so tubulin is not strongly depleted in the aster interior. We propose that the limiting component for microtubule assembly is a MAP that inhibits depolymerization, and that egg asters are tuned to low microtubule density.

Microtubule-dependent pushing forces contribute to long-distance aster movement and centration in Xenopus laevis egg extracts

During interphase of the eukaryotic cell cycle, the microtubule (MT) cytoskeleton serves as both a supportive scaffold for organelles and an arborized system of tracks for intracellular transport. At the onset of mitosis, the position of the astral MT network, specifically its center, determines the eventual location of the spindle apparatus and ultimately the cytokinetic furrow. Positioning of the MT aster often results in its movement to the center of a cell, even in large blastomeres hundreds of microns in diameter. This translocation requires positioning forces, yet how these forces are generated and then integrated within cells of various sizes and geometries remains an open question. Here we describe a method that combines microfluidics, hydrogels, and Xenopus laevis egg extract to investigate the mechanics of aster movement and centration. We determined that asters were able to find the center of artificial channels and annular cylinders, even when cytoplasmic dynein-dependent pulling mechanisms were inhibited. Characterization of aster movement away from V-shaped hydrogel barriers provided additional evidence for a MT-based pushing mechanism. Importantly, the distance over which this mechanism seemed to operate was longer than that predicted by radial aster growth models, agreeing with recent models of a more complex MT network architecture within the aster.

Stoichiometric interactions explain spindle dynamics and scaling across 100 million years of nematode evolution

The spindle shows remarkable diversity, and changes in an integrated fashion, as cells vary over evolution. Here, we provide a mechanistic explanation for variations in the first mitotic spindle in nematodes. We used a combination of quantitative genetics and biophysics to rule out broad classes of models of the regulation of spindle length and dynamics, and to establish the importance of a balance of cortical pulling forces acting in different directions. These experiments led us to construct a model of cortical pulling forces in which the stoichiometric interactions of microtubules and force generators (each force generator can bind only one microtubule), is key to explaining the dynamics of spindle positioning and elongation, and spindle final length and scaling with cell size. This model accounts for variations in all the spindle traits we studied here, both within species and across nematode species spanning over 100 million years of evolution.

Mechanisms of spindle assembly and size control

The spindle is crucial for cell division by allowing the faithful segregation of replicated chromosomes to daughter cells. Proper segregation is ensured only if microtubules (MTs) and hundreds of other associated factors interact to assemble this complex structure with the appropriate architecture and size. In this review, we describe the latest view of spindle organisation as well as the molecular gradients and mechanisms underlying MT nucleation and spindle assembly. We then discuss the overlapping physical and molecular constraints that dictate spindle morphology, concluding with a focus on spindle size regulation.

Active forces shape the metaphase spindle through a mechanical instability

The metaphase spindle is a dynamic structure orchestrating chromosome segregation during cell division. Recently, soft matter approaches have shown that the spindle behaves as an active liquid crystal. Still, it remains unclear how active force generation contributes to its characteristic spindle-like shape. Here we combine theory and experiments to show that molecular motor-driven forces shape the structure through a barreling-type instability. We test our physical model by titrating dynein activity in Xenopus egg extract spindles and quantifying the shape and microtubule orientation. We conclude that spindles are shaped by the interplay between surface tension, nematic elasticity, and motor-driven active forces. Our study reveals how motor proteins can mold liquid crystalline droplets and has implications for the design of active soft materials.

Differences in Intrinsic Tubulin Dynamic Properties Contribute to Spindle Length Control in Xenopus Species

The function of cellular organelles relates not only to their molecular composition but also to their size. However, how the size of dynamic mesoscale structures is established and maintained remains poorly understood [1-3]. Mitotic spindle length, for example, varies several-fold among cell types and among different organisms [4]. Although most studies on spindle size control focus on changes in proteins that regulate microtubule dynamics [5-8], the contribution of the spindle's main building block, the αβ-tubulin heterodimer, has yet to be studied. Apart from microtubule-associated proteins and motors, two factors have been shown to contribute to the heterogeneity of microtubule dynamics: tubulin isoform composition [9, 10] and post-translational modifications [11]. In the past, studying the contribution of tubulin and microtubules to spindle assembly has been limited by the fact that physiologically relevant tubulins were not available. Here, we show that tubulins purified from two closely related frogs, Xenopus laevis and Xenopus tropicalis, have surprisingly different microtubule dynamics in vitro. X. laevis microtubules combine very fast growth and infrequent catastrophes. In contrast, X. tropicalis microtubules grow slower and catastrophe more frequently. We show that spindle length and microtubule mass can be controlled by titrating the ratios of the tubulins from the two frog species. Furthermore, we combine our in vitro reconstitution assay and egg extract experiments with computational modeling to show that differences in intrinsic properties of different tubulins contribute to the control of microtubule mass and therefore set steady-state spindle length.

Biochemical reconstitution of branching microtubule nucleation

Microtubules are nucleated from specific locations at precise times in the cell cycle. However, the factors that constitute these microtubule nucleation pathways and their mode of action still need to be identified. Using purified Xenopus laevis proteins we biochemically reconstitute branching microtubule nucleation, which is critical for chromosome segregation. We found that besides the microtubule nucleator gamma-tubulin ring complex (γ-TuRC), the branching effectors augmin and TPX2 are required to efficiently nucleate microtubules from pre-existing microtubules. TPX2 has the unexpected capacity to directly recruit γ-TuRC as well as augmin, which in turn targets more γ-TuRC along the microtubule lattice. TPX2 and augmin enable γ-TuRC-dependent microtubule nucleation at preferred branching angles of less than 90 degrees from regularly-spaced patches along microtubules. This work provides a blueprint for other microtubule nucleation pathways and helps explain how microtubules are generated in the spindle.

Phase separation of TPX2 enhances and spatially coordinates microtubule nucleation

Phase separation of substrates and effectors is proposed to enhance biological reaction rates and efficiency. Targeting protein for Xklp2 (TPX2) is an effector of branching microtubule nucleation in spindles and functions with the substrate tubulin by an unknown mechanism. Here we show that TPX2 phase separates into a co-condensate with tubulin, which mediates microtubule nucleation in vitro and in isolated cytosol. TPX2-tubulin co-condensation preferentially occurs on pre-existing microtubules, the site of branching microtubule nucleation, at the endogenous and physiologically relevant concentration of TPX2. Truncation and chimera versions of TPX2 suggest that TPX2-tubulin co-condensation enhances the efficiency of TPX2-mediated branching microtubule nucleation. Finally, the known inhibitor of TPX2, the importin-α/β heterodimer, regulates TPX2 condensation in vitro and, consequently, branching microtubule nucleation activity in isolated cytosol. Our study demonstrates how regulated phase separation can simultaneously enhance reaction efficiency and spatially coordinate microtubule nucleation, which may facilitate rapid and accurate spindle formation.

Biochemical reconstitution of branching microtubule nucleation

Microtubules are nucleated from specific locations at precise times in the cell cycle. However, the factors that constitute these microtubule nucleation pathways and their mode of action still need to be identified. Using purified Xenopus laevis proteins we biochemically reconstitute branching microtubule nucleation, which is critical for chromosome segregation. We found that besides the microtubule nucleator gamma-tubulin ring complex (γ-TuRC), the branching effectors augmin and TPX2 are required to efficiently nucleate microtubules from pre-existing microtubules. TPX2 has the unexpected capacity to directly recruit γ-TuRC as well as augmin, which in turn targets more γ-TuRC along the microtubule lattice. TPX2 and augmin enable γ-TuRC-dependent microtubule nucleation at preferred branching angles of less than 90 degrees from regularly-spaced patches along microtubules. This work provides a blueprint for other microtubule nucleation pathways and helps explain how microtubules are generated in the spindle.

A Mechanistic View of Collective Filament Motion in Active Nematic Networks

Protein filament networks are structures crucial for force generation and cell shape. A central open question is how collective filament dynamics emerges from interactions between individual network constituents. To address this question, we study a minimal but generic model for a nematic network in which filament sliding is driven by the action of motor proteins. Our theoretical analysis shows how the interplay between viscous drag on filaments and motor-induced forces governs force propagation through such interconnected filament networks. We find that the ratio between these antagonistic forces establishes the range of filament interaction, which determines how the local filament velocity depends on the polarity of the surrounding network. This force-propagation mechanism implies that the polarity-independent sliding observed in Xenopus egg extracts and in vitro experiments with purified components is a consequence of a large force-propagation length. We suggest how our predictions can be tested by tangible in vitro experiments whose feasibility is assessed with the help of simulations and an accompanying theoretical analysis.

Predicted Effects of Severing Enzymes on the Length Distribution and Total Mass of Microtubules

Microtubules are dynamic cytoskeletal polymers whose growth and shrinkage are highly regulated as eukaryotic cells change shape, move, and divide. One family of microtubule regulators includes the ATP-hydrolyzing enzymes spastin, katanin, and fidgetin, which sever microtubule polymers into shorter fragments. Paradoxically, severases can increase microtubule number and mass in cells. Recent work with purified spastin and katanin accounts for this phenotype by showing that, in addition to severing, these enzymes modulate microtubule dynamics by accelerating the conversion of microtubules from their shrinking to their growing states and thereby promoting their regrowth. This leads to the observed exponential increase in microtubule mass. Spastin also influences the steady-state distribution of microtubule lengths, changing it from an exponential, as predicted by models of microtubule dynamic instability, to a peaked distribution. This effect of severing and regrowth by spastin on the microtubule length distribution has not been explained theoretically. To solve this problem, we formulated and solved a master equation for the time evolution of microtubule lengths in the presence of severing and microtubule dynamic instability. We then obtained numerical solutions to the steady-state length distribution and showed that the rate of severing and the speed of microtubule growth are the dominant parameters determining the steady-state length distribution. Furthermore, we found that the amplification rate is predicted to increase with severing, which is, to our knowledge, a new result. Our results establish a theoretical basis for how severing and dynamics together can serve to nucleate new microtubules, constituting a versatile mechanism to regulate microtubule length and mass.

How to tune spindle size relative to cell size?

Cells need to regulate the size and shape of their organelles for proper function. For example, the mitotic spindle adapts its size to changes in cell size over several orders of magnitude, but we lack a mechanistic understanding of how this is achieved. Here, we review our current knowledge of how small and large spindles assemble and ask which microtubule-based biophysical processes (nucleation, polymerization dynamics, transport) may be responsible for spindle size regulation. Finally, we review possible cell-scale mechanisms that put spindle size under the regulation of cell size.

Direct observation of branching MT nucleation in living animal cells

Branching microtubule nucleation by its molecular mediators has never been directly observed in animal cells. By imaging augmin, γ-TuRC, and microtubules with high spatiotemporal resolution, Verma and Maresca quantitatively define the sequential steps of augmin-mediated branching microtubule nucleation in dividing Drosophila cells.

Centrosome-mediated microtubule (MT) nucleation has been well characterized; however, numerous noncentrosomal MT nucleation mechanisms exist. The branching MT nucleation pathway envisages that the γ-tubulin ring complex (γ-TuRC) is recruited to MTs by the augmin complex to initiate nucleation of new MTs. While the pathway is well conserved at a molecular and functional level, branching MT nucleation by core constituents has never been directly observed in animal cells. Here, multicolor TIRF microscopy was applied to visualize and quantitatively define the entire process of branching MT nucleation in dividing Drosophila cells during anaphase. The steps of a stereotypical branching nucleation event entailed augmin binding to a mother MT and recruitment of γ-TuRC after 15 s, followed by nucleation 16 s later of a daughter MT at a 36° branch angle. Daughters typically remained attached throughout their ∼40-s lifetime unless the mother depolymerized past the branch point. Assembly of branched MT arrays, which did not require Drosophila TPX2, enhanced localized RhoA activation during cytokinesis.

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.

Induction of a Spindle-Assembly-Competent M Phase in Xenopus Egg Extracts

Normal mitotic spindle assembly is a prerequisite for faithful chromosome segregation and unperturbed cell-cycle progression. Precise functioning of the spindle machinery relies on conserved architectural features, such as focused poles, chromosome alignment at the metaphase plate, and proper spindle length. These morphological requirements can be achieved only within a compositionally distinct cytoplasm that results from cell-cycle-dependent regulation of specific protein levels and specific post-translational modifications. Here, we used cell-free extracts derived from Xenopus laevis eggs to recapitulate different phases of the cell cycle in vitro and to determine which components are required to render interphase cytoplasm spindle-assembly competent in the absence of protein translation. We found that addition of a nondegradable form of the master cell-cycle regulator cyclin B1 can indeed induce some biochemical and phenomenological characteristics of mitosis, but cyclin B1 alone is insufficient and actually deleterious at high levels for normal spindle assembly. In contrast, addition of a phosphomimetic form of the Greatwall-kinase effector Arpp19 with a specific concentration of nondegradable cyclin B1 rescued spindle bipolarity but resulted in larger-than-normal bipolar spindles with a misalignment of chromosomes. Both were corrected by the addition of exogenous Xkid (Xenopus homolog of human Kid/KIF22), indicating a role for this chromokinesin in regulating spindle length. These observations suggest that, of the many components degraded at mitotic exit and then replenished during the subsequent interphase, only a few are required to induce a cell-cycle transition that produces a spindle-assembly-competent cytoplasm.

Direct induction of microtubule branching by microtubule nucleation factor SSNA1

Microtubules are central elements of the eukaryotic cytoskeleton that often function as part of branched networks. Current models for branching include nucleation of new microtubules from severed microtubule seeds or from gamma-tubulin recruited to the side of a pre-existing microtubule. Here, we found that microtubules can be directly remodeled into branched structures by the microtubule-remodeling factor SSNA1 (or also NA14/DIP13). The branching activity of SSNA1 relies on its ability to self-assemble into fibrils in a head-to-tail fashion. SSNA1 fibrils guide protofilaments of a microtubule to split apart to form daughter microtubules. We further found that SSNA1 localizes at axon branching sites and has a key role in neuronal development. SSNA1 mutants that abolish microtubule branching in vitro also fail to promote axon development and branching when overexpressed in neurons. We have therefore, discovered a mechanism for microtubule-branching and implicated its role in neuronal development.

A Switch in Microtubule Orientation during C. elegans Meiosis

In oocytes of many organisms, meiotic spindles form in the absence of centrosomes [1-5]. Such female meiotic spindles have a pointed appearance in metaphase with microtubules focused at acentrosomal spindle poles. At anaphase, the microtubules of acentrosomal spindles then transition to an inter-chromosomal array, while the spindle poles disappear. This transition is currently not understood. Previous studies have focused on this inter-chromosomal microtubule array and proposed a pushing model to drive chromosome segregation [6, 7]. This model includes an end-on orientation of microtubules with chromosomes. Alternatively, chromosomes were thought to associate along bundles of microtubules [8, 9]. Starting with metaphase, this second model proposed a pure lateral chromosome-to-microtubule association up to the final meiotic stages of anaphase. Here, we applied large-scale electron tomography [10] of staged C. elegans oocytes in meiosis to analyze the orientation of microtubules in respect to chromosomes. We show that microtubules at metaphase I are primarily oriented laterally to the chromosomes and that microtubules switch to an end-on orientation during progression through anaphase. We further show that this switch in microtubule orientation involves a kinesin-13 microtubule depolymerase, KLP-7, which removes laterally associated microtubules around chromosomes. From this, we conclude that both lateral and end-on modes of microtubule-to-chromosome orientations are successively used in C. elegans oocytes to segregate meiotic chromosomes.

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.

Molecular force spectroscopy of kinetochore-microtubule attachment in silico: Mechanical signatures of an unusual catch bond and collective effects

Measurement of the lifetime of attachments formed by a single microtubule (MT) with a single kinetochore (kt) in vitro under force-clamp conditions had earlier revealed a catch-bond-like behavior. In the past, the physical origin of this apparently counterintuitive phenomenon was traced to the nature of the force dependence of the (de)polymerization kinetics of the MTs. Here, first the same model MT-kt attachment is subjected to external tension that increases linearly with time until rupture occurs. In our force-ramp experiments in silico, the model displays the well known "mechanical signatures" of a catch bond probed by molecular force spectroscopy. Exploiting this evidence, we have further strengthened the analogy between MT-kt attachments and common ligand-receptor bonds in spite of the crucial differences in their underlying physical mechanisms. We then extend the formalism to model the stochastic kinetics of an attachment formed by a bundle of multiple parallel microtubules with a single kt considering the effect of rebinding under force-clamp and force-ramp conditions. From numerical studies of the model we predict the trends of variation of the mean lifetime and mean rupture force with the increasing number of MTs in the bundle. Both the mean lifetime and the mean rupture force display nontrivial nonlinear dependence on the maximum number of MTs that can attach simultaneously to the same kt.