The Physics of the Metaphase Spindle

Unveiling inter-embryo variability in spindle length over time: Towards quantitative phenotype analysis

How can inter-individual variability be quantified? Measuring many features per experiment raises the question of choosing them to recapitulate high-dimensional data. Tackling this challenge on spindle elongation phenotypes, we showed that only three typical elongation patterns describe spindle elongation in C. elegans one-cell embryo. These archetypes, automatically extracted from the experimental data using principal component analysis (PCA), accounted for more than 95% of inter-individual variability of more than 1600 experiments across more than 100 different conditions. The two first archetypes were related to spindle average length and anaphasic elongation rate. The third archetype, accounting for 6% of the variability, was novel and corresponded to a transient spindle shortening in late metaphase, reminiscent of kinetochore function-defect phenotypes. Importantly, these three archetypes were robust to the choice of the dataset and were found even considering only non-treated conditions. Thus, the inter-individual differences between genetically perturbed embryos have the same underlying nature as natural inter-individual differences between wild-type embryos, independently of the temperatures. We thus propose that beyond the apparent complexity of the spindle, only three independent mechanisms account for spindle elongation, weighted differently in the various conditions. Interestingly, the spindle-length archetypes covered both metaphase and anaphase, suggesting that spindle elongation in late metaphase is sufficient to predict the late anaphase length. We validated this idea using a machine-learning approach. Finally, given amounts of these three archetypes could represent a quantitative phenotype. To take advantage of this, we set out to predict interacting genes from a seed based on the PCA coefficients. We exemplified this firstly on the role of tpxl-1 whose homolog tpx2 is involved in spindle microtubule branching, secondly the mechanism regulating metaphase length, and thirdly the central spindle players which set the length at anaphase. We found novel interactors not in public databases but supported by recent experimental publications.

Antiparallel microtubule bundling supports KIF15-driven mitotic spindle assembly

The spindle is a bipolar microtubule-based machine that is crucial for accurate chromosome segregation. Spindle bipolarity is generated by Eg5 (a kinesin-5), a conserved motor that drives spindle assembly by localizing to and sliding apart antiparallel microtubules. In the presence of Eg5 inhibitors (K5Is), KIF15 (a kinesin-12) can promote spindle assembly, resulting in K5I-resistant cells (KIRCs). However, KIF15 is a less potent motor than Eg5, suggesting that other factors may contribute to spindle formation in KIRCs. Protein Regulator of Cytokinesis 1 (PRC1) preferentially bundles antiparallel microtubules, and we previously showed that PRC1 promotes KIF15-microtubule binding, leading us to hypothesize that PRC1 may enhance KIF15 activity in KIRCs. Here, we demonstrate that: 1) loss of PRC1 in KIRCs decreases spindle bipolarity, 2) overexpression of PRC1 increases spindle formation efficiency in KIRCs, 3) overexpression of PRC1 protects K5I naïve cells against the K5I S-trityl-L-cysteine (STLC), and 4) PRC1 overexpression promotes the establishment of K5I resistance. These effects are not fully reproduced by a TPX2, a microtubule bundler with no known preference for microtubule orientation. These results suggest a model wherein PRC1-mediated bundling of microtubules creates a more favorable microtubule architecture for KIF15-driven mitotic spindle assembly in the context of Eg5 inhibition.

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.

Computational Studies Reveal How Passive Cross-Linkers Regulate Anaphase Spindle Elongation

In eukaryotic cell division, a series of events are organized to produce two daughter cells. The spindle elongation in anaphase B is essential for providing enough space to maintain cell size and distribute sister chromatids properly, which is associated with microtubules and microtubule-associated proteins such as kinesin-5 Eg5 and the Ase1-related protein, PRC1. The available experimental data indicated that after the start of anaphase B more PRC1 proteins can bind to the antiparallel microtubule pairs in the spindle but the excess amount of PRC1 proteins can lead to the failure of cell division, indicating that PRC1 proteins can regulate the spindle elongation in a concentration-dependent manner. However, the underlying mechanism of the PRC1 proteins regulating the spindle elongation has not been explained up to now. Here, we use a simplified model, where only the two important participants (kinesin-5 Eg5 motors and PRC1 proteins) are considered, to study the spindle elongation during anaphase B. We first show that only in the appropriate range of the PRC1 concentration can the spindle elongation complete properly. Furthermore, we explore the underlying mechanism of PRC1 as a regulator for spindle elongation.

Sliding of antiparallel microtubules drives bipolarization of monoastral spindles

Time-lapse imaging with liquid crystal polarized light (LC-PolScope) and fluorescent speckle microscopy (FSM) enabled this study of spindle microtubules in monoastral spindles that were produced in crane-fly spermatocytes through flattening-induced centrosome displacement. Monoastral spindles are found in several other contexts: after laser ablation of one of a cell's two centrosomes (in the work of Khodjakov et al.), in Drosophila "urchin" mutants (in the works of Heck et al. and of Wilson et al.), in Sciara males (in the works of Fuge and of Metz), and in RNAi variants of Drosophila S2 cells (in the work of Goshima et al.). In all cases, just one pole has a centrosome (the astral pole); the other lacks a centrosome (the anastral pole). Thus, the question: How is the anastral half-spindle, lacking a centrosome, constructed? We learned that monoastral spindles are assembled in two phases: Phase I assembles the astral half-spindle composed of centrosomal microtubules, and Phase II assembles microtubules of the anastral half through extension of new microtubule polymerization outward from the spindle's equatorial mid-zone. That process uses plus ends of existing centrosomal microtubules as guiding templates to assemble anastral microtubules of opposite polarity. Anastral microtubules slide outward with their minus ends leading, thereby establishing proper bipolarity just like in normal biastral spindles that have two centrosomes.

Fast backward steps and detachment of single kinesin molecules measured under a wide range of loads

To understand force generation under a wide range of loads, the stepping of single kinesin molecules was measured at loads from -20 to 42 pN by optical tweezers with high temporal resolution. The optical trap has been improved to halve positional noise and increase bandwidth by using 200-nm beads. The step size of the forward and backward steps was 8.2 nm even over a wide range of loads. Histograms of the dwell times of backward steps and detachment fit well to two independent exponential equations with fast (~0.4 ms) and slow (>3 ms) time constants, indicating the existence of a fast step in addition to the conventional slow step. The dwell times of the fast steps were almost independent of the load and ATP concentration, while those of the slow backward steps and detachment depended on those. We constructed the kinetic model to explain the fast and slow steps under a wide range of loads.

Synergy between inhibitors of two mitotic spindle assembly motors undermines an adaptive response

Mitosis is the cellular process that ensures accurate segregation of the cell's genetic material into two daughter cells. Mitosis is often deregulated in cancer; thus drugs that target mitosis-specific proteins represent attractive targets for anticancer therapy. Numerous inhibitors have been developed against kinesin-5 Eg5, a kinesin essential for bipolar spindle assembly. Unfortunately, Eg5 inhibitors (K5Is) have been largely ineffective in the clinic, possibly due to the activity of a second kinesin, KIF15, that can suppress the cytotoxic effect of K5Is by driving spindle assembly through an Eg5-independent pathway. We hypothesized that pairing of K5Is with small molecule inhibitors of KIF15 will be more cytotoxic than either inhibitor alone. Here we present the results of a high-throughput screen from which we identified two inhibitors that inhibit the motor activity of KIF15 both in vitro and in cells. These inhibitors selectively inhibit KIF15 over other molecular motors and differentially affect the ability of KIF15 to bind microtubules. Finally, we find that chemical inhibition of KIF15 reduces the ability of cells to acquire resistance to K5Is, highlighting the centrality of KIF15 to K5I resistance and the value of these inhibitors as tools with which to study KIF15 in a physiological context.

Modeling and mechanical perturbations reveal how spatially regulated anchorage gives rise to spatially distinct mechanics across the mammalian spindle

During cell division, the spindle generates force to move chromosomes. In mammals, microtubule bundles called kinetochore-fibers (k-fibers) attach to and segregate chromosomes. To do so, k-fibers must be robustly anchored to the dynamic spindle. We previously developed microneedle manipulation to mechanically challenge k-fiber anchorage, and observed spatially distinct response features revealing the presence of heterogeneous anchorage (Suresh et al., 2020). How anchorage is precisely spatially regulated, and what forces are necessary and sufficient to recapitulate the k-fiber's response to force remain unclear. Here, we develop a coarse-grained k-fiber model and combine with manipulation experiments to infer underlying anchorage using shape analysis. By systematically testing different anchorage schemes, we find that forces solely at k-fiber ends are sufficient to recapitulate unmanipulated k-fiber shapes, but not manipulated ones for which lateral anchorage over a 3 μm length scale near chromosomes is also essential. Such anchorage robustly preserves k-fiber orientation near chromosomes while allowing pivoting around poles. Anchorage over a shorter length scale cannot robustly restrict pivoting near chromosomes, while anchorage throughout the spindle obstructs pivoting at poles. Together, this work reveals how spatially regulated anchorage gives rise to spatially distinct mechanics in the mammalian spindle, which we propose are key for function.

Microtubule organization and cell geometry

A characteristic feature of nondividing animal cells is the radial organization of microtubules (MTs), emanating from a single microtubule organizing center (MTOC). As generically these cells are not spherically symmetric, this raises the question of the influence of cell geometry on the orientational distribution of microtubules. We present a systematic study of this question in a simplified setting where MTs are nucleated from a single fixed MTOC in the center of an elliptical cell geometry. Within this context we introduce four models of increasing complexity, each one introducing additional mechanisms that govern the interaction of the MTs with the cell boundary. In order, we consider the cases: MTs that can bind to the boundary with a fixed mean residence time (M0), force-producing MTs that can slide on the boundary towards the cell poles (MS), MTs that interact with a generic polarity factor that is transported and deposited at the boundary, and which in turn stabilizes the MTs at the boundary (MP), and a final model in which both sliding and stabilization by polarity factors is taken into account (MSP). In the baseline model (M0), the exponential length distribution of MTs causes most of the interactions at the cell boundary to occur along the shorter transverse direction in the cell, leading to transverse biaxial order. MT sliding (MS) is able to reorient the main axis of this biaxial order along the longitudinal axis. The polarization mechanism introduced in MP and MSP overrules the geometric bias towards bipolar order observed in M0 and MS, and allows the establishment of unipolar order either along the short (MP) or the long cell axis (MSP). The behavior of the latter two models can be qualitatively reproduced by a very simple toy model with discrete MT orientations.

Cross-linker design determines microtubule network organization by opposing motors

During cell division, cross-linking motors determine the architecture of the spindle, a dynamic microtubule network that segregates the chromosomes in eukaryotes. It is unclear how motors with opposite directionality coordinate to drive both contractile and extensile behaviors in the spindle. Particularly, the impact of different cross-linker designs on network self-organization is not understood, limiting our understanding of self-organizing structures in cells but also our ability to engineer new active materials. Here, we use experiment and theory to examine active microtubule networks driven by mixtures of motors with opposite directionality and different cross-linker design. We find that although the kinesin-14 HSET causes network contraction when dominant, it can also assist the opposing kinesin-5 KIF11 to generate extensile networks. This bifunctionality results from HSET's asymmetric design, distinct from symmetric KIF11. These findings expand the set of rules underlying patterning of active microtubule assemblies and allow a better understanding of motor cooperation in the spindle.

A mitotic chromatin phase transition prevents perforation by microtubules

Dividing eukaryotic cells package extremely long chromosomal DNA molecules into discrete bodies to enable microtubule-mediated transport of one genome copy to each of the newly forming daughter cells^1–3. Assembly of mitotic chromosomes involves DNA looping by condensin^4–8 and chromatin compaction by global histone deacetylation^9–13. Although condensin confers mechanical resistance to spindle pulling forces^14–16, it is not known how histone deacetylation affects material properties and, as a consequence, segregation mechanics of mitotic chromosomes. Here we show how global histone deacetylation at the onset of mitosis induces a chromatin-intrinsic phase transition that endows chromosomes with the physical characteristics necessary for their precise movement during cell division. Deacetylation-mediated compaction of chromatin forms a structure dense in negative charge and allows mitotic chromosomes to resist perforation by microtubules as they are pushed to the metaphase plate. By contrast, hyperacetylated mitotic chromosomes lack a defined surface boundary, are frequently perforated by microtubules and are prone to missegregation. Our study highlights the different contributions of DNA loop formation and chromatin phase separation to genome segregation in dividing cells.

Histone deacetylation at the onset of mitosis induces a chromatin-intrinsic phase transition that endows chromosomes with the physical characteristics necessary for their precise movement during cell division.

Three-dimensional structure of kinetochore-fibers in human mitotic spindles

During cell division, kinetochore microtubules (KMTs) provide a physical linkage between the chromosomes and the rest of the spindle. KMTs in mammalian cells are organized into bundles, so-called kinetochore-fibers (k-fibers), but the ultrastructure of these fibers is currently not well characterized. Here, we show by large-scale electron tomography that each k-fiber in HeLa cells in metaphase is composed of approximately nine KMTs, only half of which reach the spindle pole. Our comprehensive reconstructions allowed us to analyze the three-dimensional (3D) morphology of k-fibers and their surrounding MTs in detail. We found that k-fibers exhibit remarkable variation in circumference and KMT density along their length, with the pole-proximal side showing a broadening. Extending our structural analysis then to other MTs in the spindle, we further observed that the association of KMTs with non-KMTs predominantly occurs in the spindle pole regions. Our 3D reconstructions have implications for KMT growth and k-fiber self-organization models as covered in a parallel publication applying complementary live-cell imaging in combination with biophysical modeling (Conway et al., 2022). Finally, we also introduce a new visualization tool allowing an interactive display of our 3D spindle data that will serve as a resource for further structural studies on mitosis in human cells.

Self-organization of kinetochore-fibers in human mitotic spindles

During eukaryotic cell division, chromosomes are linked to microtubules (MTs) in the spindle by a macromolecular complex called the kinetochore. The bound kinetochore microtubules (KMTs) are crucial to ensuring accurate chromosome segregation. Recent reconstructions by electron tomography (Kiewisz et al., 2022) captured the positions and configurations of every MT in human mitotic spindles, revealing that roughly half the KMTs in these spindles do not reach the pole. Here, we investigate the processes that give rise to this distribution of KMTs using a combination of analysis of large-scale electron tomography, photoconversion experiments, quantitative polarized light microscopy, and biophysical modeling. Our results indicate that in metaphase, KMTs grow away from the kinetochores along well-defined trajectories, with the speed of the KMT minus ends continually decreasing as the minus ends approach the pole, implying that longer KMTs grow more slowly than shorter KMTs. The locations of KMT minus ends, and the turnover and movements of tubulin in KMTs, are consistent with models in which KMTs predominately nucleate de novo at kinetochores in metaphase and are inconsistent with substantial numbers of non-KMTs being recruited to the kinetochore in metaphase. Taken together, this work leads to a mathematical model of the self-organization of kinetochore-fibers in human mitotic spindles.

Crowder and surface effects on self-organization of microtubules

Microtubules are an essential physical building block of cellular systems. They are organized using specific crosslinkers, motors, and influencers of nucleation and growth. With the addition of antiparallel crosslinkers, microtubule self-organization patterns go through a transition from fanlike structures to homogeneous tactoid condensates in vitro. Tactoids are reminiscent of biological mitotic spindles, the cell division machinery. To create these organizations, we previously used polymer crowding agents. Here we study how altering the properties of the crowders, such as type, size, and molecular weight, affects microtubule organization. Comparing simulations with experiments, we observe a scaling law associated with the fanlike patterns in the absence of crosslinkers. Tactoids formed in the presence of crosslinkers show variable length, depending on the crowders. We correlate the subtle differences to filament contour length changes, affected by nucleation and growth rate changes induced by the polymers in solution. Using quantitative image analysis, we deduce that the tactoids differ from traditional liquid crystal organization, as they are limited in width irrespective of crowders and surfaces, and behave as solidlike condensates.

Fundamentals of the logarithmic measure for revealing multimodal diffusion

We develop a theoretical foundation for a time-series analysis method suitable for revealing the spectrum of diffusion coefficients in mixed Brownian systems, for which no prior knowledge of particle distinction is required. This method is directly relevant for particle tracking in biological systems, in which diffusion processes are often nonuniform. We transform Brownian data onto the logarithmic domain, in which the coefficients for individual modes of diffusion appear as distinct spectral peaks in the probability density. We refer to the method as the logarithmic measure of diffusion, or simply as the logarithmic measure. We provide a general protocol for deriving analytical expressions for the probability densities on the logarithmic domain. The protocol is applicable for any number of spatial dimensions with any number of diffusive states. The analytical form can be fitted to data to reveal multiple diffusive modes. We validate the theoretical distributions and benchmark the accuracy and sensitivity of the method by extracting multimodal diffusion coefficients from two-dimensional Brownian simulations of polydisperse filament bundles. Bundling the filaments allows us to control the system nonuniformity and hence quantify the sensitivity of the method. By exploiting the anisotropy of the simulated filaments, we generalize the logarithmic measure to rotational diffusion. By fitting the analytical forms to simulation data, we confirm the method's theoretical foundation. An error analysis in the single-mode regime shows that the proposed method is comparable in accuracy to the standard mean-squared displacement approach for evaluating diffusion coefficients. For the case of multimodal diffusion, we compare the logarithmic measure against other, more sophisticated methods, showing that both model selectivity and extraction accuracy are comparable for small data sets. Therefore, we suggest that the logarithmic measure, as a method for multimodal diffusion coefficient extraction, is ideally suited for small data sets, a condition often confronted in the experimental context. Finally, we critically discuss the proposed benefits of the method and its information content.

Mechanical Mechanisms of Chromosome Segregation

Chromosome segregation—the partitioning of genetic material into two daughter cells—is one of the most crucial processes in cell division. In all Eukaryotes, chromosome segregation is driven by the spindle, a microtubule-based, self-organizing subcellular structure. Extensive research performed over the past 150 years has identified numerous commonalities and contrasts between spindles in different systems. In this review, we use simple coarse-grained models to organize and integrate previous studies of chromosome segregation. We discuss sites of force generation in spindles and fundamental mechanical principles that any understanding of chromosome segregation must be based upon. We argue that conserved sites of force generation may interact differently in different spindles, leading to distinct mechanical mechanisms of chromosome segregation. We suggest experiments to determine which mechanical mechanism is operative in a particular spindle under study. Finally, we propose that combining biophysical experiments, coarse-grained theories, and evolutionary genetics will be a productive approach to enhance our understanding of chromosome segregation in the future.

Functional reciprocity of proteins involved in mitosis and endocytosis

Mitosis and endocytosis are two fundamental cellular processes essential for maintaining a eukaryotic life. Mitosis partitions duplicated chromatin enveloped in the nuclear membrane into two new cells, whereas endocytosis takes in extracellular substances through membrane invagination. These two processes are spatiotemporally separated and seemingly unrelated. However, recent studies have uncovered that endocytic proteins have moonlighting functions in mitosis, and mitotic complexes manifest additional roles in endocytosis. In this review, we summarize important proteins or protein complexes that participate in both processes, compare their mechanism of action, and discuss the rationale behind this multifunctionality. We also speculate on the possible origin of the functional reciprocity from an evolutionary perspective.

Mechanobiology of the Mitotic Spindle

The mitotic spindle is a microtubule-based assembly that separates the chromosomes during cell division. As the spindle is basically a mechanical micro machine, the understanding of its functioning is constantly motivating the development of experimental approaches based on mechanical perturbations, which are complementary to and work together with the classical genetics and biochemistry methods. Recent data emerging from these approaches in combination with theoretical modeling led to novel ideas and significant revisions of the basic concepts in the field. In this Perspective, we discuss the advances in the understanding of spindle mechanics, focusing on microtubule forces that control chromosome movements.

Genetic Material Manipulation and Modification by Optical Trapping and Nanosurgery-A Perspective

Light can be employed as a tool to alter and manipulate matter in many ways. An example has been the implementation of optical trapping, the so called optical tweezers, in which light can hold and move small objects with 3D control. Of interest for the Life Sciences and Biotechnology is the fact that biological objects in the size range from tens of nanometers to hundreds of microns can be precisely manipulated through this technology. In particular, it has been shown possible to optically trap and move genetic material (DNA and chromatin) using optical tweezers. Also, these biological entities can be severed, rearranged and reconstructed by the combined use of laser scissors and optical tweezers. In this review, the background, current state and future possibilities of optical tweezers and laser scissors to manipulate, rearrange and alter genetic material (DNA, chromatin and chromosomes) will be presented. Sources of undesirable effects by the optical procedure and measures to avoid them will be discussed. In addition, first tentative approaches at cellular-level genetic and organelle surgery, in which genetic material or DNA-carrying organelles are extracted out or introduced into cells, will be presented.

Individual kinetochore-fibers locally dissipate force to maintain robust mammalian spindle structure

At cell division, the mammalian kinetochore binds many spindle microtubules that make up the kinetochore-fiber. To segregate chromosomes, the kinetochore-fiber must be dynamic and generate and respond to force. Yet, how it remodels under force remains poorly understood. Kinetochore-fibers cannot be reconstituted in vitro, and exerting controlled forces in vivo remains challenging. Here, we use microneedles to pull on mammalian kinetochore-fibers and probe how sustained force regulates their dynamics and structure. We show that force lengthens kinetochore-fibers by persistently favoring plus-end polymerization, not by increasing polymerization rate. We demonstrate that force suppresses depolymerization at both plus and minus ends, rather than sliding microtubules within the kinetochore-fiber. Finally, we observe that kinetochore-fibers break but do not detach from kinetochores or poles. Together, this work suggests an engineering principle for spindle structural homeostasis: different physical mechanisms of local force dissipation by the k-fiber limit force transmission to preserve robust spindle structure. These findings may inform how other dynamic, force-generating cellular machines achieve mechanical robustness.

Mechanics of the spindle apparatus

During mitosis microtubules self-organize to form a bipolar mitotic spindle structure, which positions the sister chromatids on the spindle mid-plane and separates them afterwards. Previous studies have identified many spindle associated proteins. Yet, we do not fully understand how these nanoscopic proteins lead to force generation through interactions of individual microtubules, motor proteins and chromosomes, and how a large number of these local interactions ultimately determine the structure and mechanics of the spindle in micron scale. Here we review the current understanding and open questions related to the structure and mechanics of the mitotic spindle. We then discuss how a combination of electron microscopy and computational modeling can be used to tackle some of these open questions.

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.

Microneedle manipulation of the mammalian spindle reveals specialized, short-lived reinforcement near chromosomes

The spindle generates force to segregate chromosomes at cell division. In mammalian cells, kinetochore-fibers connect chromosomes to the spindle. The dynamic spindle anchors kinetochore-fibers in space and time to move chromosomes. Yet, how it does so remains poorly understood as we lack tools to directly challenge this anchorage. Here, we adapt microneedle manipulation to exert local forces on the spindle with spatiotemporal control. Pulling on kinetochore-fibers reveals the preservation of local architecture in the spindle-center over seconds. Sister, but not neighbor, kinetochore-fibers remain tightly coupled, restricting chromosome stretching. Further, pulled kinetochore-fibers pivot around poles but not chromosomes, retaining their orientation within 3 μm of chromosomes. This local reinforcement has a 20 s lifetime, and requires the microtubule crosslinker PRC1. Together, these observations indicate short-lived, specialized reinforcement in the spindle center. This could help protect chromosome attachments from transient forces while allowing spindle remodeling, and chromosome movements, over longer timescales.

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.

The evolution of spindles and their mechanical implications for cancer metastasis

The mitotic spindle has long been known to play a crucial role in mitosis, orchestrating the segregation of chromosomes into two daughter cells during mitosis with high fidelity. Intracellular forces generated by the mitotic spindle are increasingly well understood, and recent work has revealed that the efficiency and the accuracy of mitosis is ensured by the scaling of mitotic spindle size with cell size. However, the role of the spindle in cancer progression has largely been ignored. Two recent studies point toward the role of mitotic spindle evolution in cancer progression through extracellular force generation. Cancer cells with lengthened spindles exhibit highly increased metastatic potential. Further, interpolar spindle elongation drives protrusive extracellular force generation along the mitotic axis to allow mitotic elongation, a morphological change that is required for cell division. Together, these findings open a new research area studying the role of the mitotic spindle evolution in cancer metastasis.

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.

A computational model of the early stages of acentriolar meiotic spindle assembly

The mitotic spindle is an ensemble of microtubules responsible for the repartition of the chromosomal content between the two daughter cells during division. In metazoans, spindle assembly is a gradual process involving dynamic microtubules and recruitment of numerous associated proteins and motors. During mitosis, centrosomes organize and nucleate the majority of spindle microtubules. In contrast, oocytes lack canonical centrosomes but are still able to form bipolar spindles, starting from an initial ball that self-organizes in several hours. Interfering with early steps of meiotic spindle assembly can lead to erroneous chromosome segregation. Although not fully elucidated, this process is known to rely on antagonistic activities of plus end- and minus end-directed motors. We developed a model of early meiotic spindle assembly in mouse oocytes, including key factors such as microtubule dynamics and chromosome movement. We explored how the balance between plus end- and minus end-directed motors, as well as the influence of microtubule nucleation, impacts spindle morphology. In a refined model, we added spatial regulation of microtubule stability and minus-end clustering. We could reproduce the features of early stages of spindle assembly from 12 different experimental perturbations and predict eight additional perturbations. With its ability to characterize and predict chromosome individualization, this model can help deepen our understanding of spindle assembly.

Microtubule End-Clustering Maintains a Steady-State Spindle Shape

Each time a cell divides, the microtubule cytoskeleton self-organizes into the metaphase spindle: an ellipsoidal steady-state structure that holds its stereotyped geometry despite microtubule turnover and internal stresses [1-6]. Regulation of microtubule dynamics, motor proteins, microtubule crosslinking, and chromatid cohesion can modulate spindle size and shape, and yet modulated spindles reach and hold a new steady state [7-11]. Here, we ask what maintains any spindle steady-state geometry. We report that clustering of microtubule ends by dynein and NuMA is essential for mammalian spindles to hold a steady-state shape. After dynein or NuMA deletion, the mitotic microtubule network is "turbulent"; microtubule bundles extend and bend against the cell cortex, constantly remodeling network shape. We find that spindle turbulence is driven by the homotetrameric kinesin-5 Eg5, and that acute Eg5 inhibition in turbulent spindles recovers spindle geometry and stability. Inspired by in vitro work on active turbulent gels of microtubules and kinesin [12, 13], we explore the kinematics of this in vivo turbulent network. We find that turbulent spindles display decreased nematic order and that motile asters distort the nematic director field. Finally, we see that turbulent spindles can drive both flow of cytoplasmic organelles and whole-cell movement-analogous to the autonomous motility displayed by droplet-encapsulated turbulent gels [12]. Thus, end-clustering by dynein and NuMA is required for mammalian spindles to reach a steady-state geometry, and in their absence Eg5 powers a turbulent microtubule network inside mitotic cells.

The Spindle: Integrating Architecture and Mechanics across Scales

The spindle segregates chromosomes at cell division, and its task is a mechanical one. While we have a nearly complete list of spindle components, how their molecular-scale mechanics give rise to cellular-scale spindle architecture, mechanics, and function is not yet clear. Recent in vitro and in vivo measurements bring new levels of molecular and physical control and shed light on this question. Highlighting recent findings and open questions, we introduce the molecular force generators of the spindle, and discuss how they organize microtubules into diverse architectural modules and give rise to the emergent mechanics of the mammalian spindle. Throughout, we emphasize the breadth of space and time scales at play, and the feedback between spindle architecture, dynamics, and mechanics that drives robust function.