Mechanical design principles of a mitotic 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.

Distinct regions of the kinesin-5 C-terminal tail are essential for mitotic spindle midzone localization and sliding force

Kinesin-5 motor proteins play essential roles during mitosis in most organisms. Their tetrameric structure and plus-end-directed motility allow them to bind to and move along antiparallel microtubules, thereby pushing spindle poles apart to assemble a bipolar spindle. Recent work has shown that the C-terminal tail is particularly important to kinesin-5 function: The tail affects motor domain structure, ATP hydrolysis, motility, clustering, and sliding force measured for purified motors, as well as motility, clustering, and spindle assembly in cells. Because previous work has focused on presence or absence of the entire tail, the functionally important regions of the tail remain to be identified. We have therefore characterized a series of kinesin-5/Cut7 tail truncation alleles in fission yeast. Partial truncation causes mitotic defects and temperature-sensitive growth, while further truncation that removes the conserved BimC motif is lethal. We compared the sliding force generated by cut7 mutants using a kinesin-14 mutant background in which some microtubules detach from the spindle poles and are pushed into the nuclear envelope. These Cut7-driven protrusions decreased as more of the tail was truncated, and the most severe truncations produced no observable protrusions. Our observations suggest that the C-terminal tail of Cut7p contributes to both sliding force and midzone localization. In the context of sequential tail truncation, the BimC motif and adjacent C-terminal amino acids are particularly important for sliding force. In addition, moderate tail truncation increases midzone localization, but further truncation of residues N-terminal to the BimC motif decreases midzone localization.

Distinct regions of the kinesin-5 C-terminal tail are essential for mitotic spindle midzone localization and sliding force

Kinesin-5 motor proteins play essential roles during mitosis in most organisms. Their tetrameric structure and plus-end-directed motility allow them to bind to and move along antiparallel microtubules, thereby pushing spindle poles apart to assemble a bipolar spindle. Recent work has shown that the C-terminal tail is particularly important to kinesin-5 function: the tail affects motor domain structure, ATP hydrolysis, motility, clustering, and sliding force measured for purified motors, as well as motility, clustering, and spindle assembly in cells. Because previous work has focused on presence or absence of the entire tail, the functionally important regions of the tail remain to be identified. We have therefore characterized a series of kinesin-5/Cut7 tail truncation alleles in fission yeast. Partial truncation causes mitotic defects and temperature-sensitive growth, while further truncation that removes the conserved BimC motif is lethal. We compared the sliding force generated by cut7 mutants using a kinesin-14 mutant background in which some microtubules detach from the spindle poles and are pushed into the nuclear envelope. These Cut7-driven protrusions decreased as more of the tail was truncated, and the most severe truncations produced no observable protrusions. Our observations suggest that the C-terminal tail of Cut7p contributes to both sliding force and midzone localization. In the context of sequential tail truncation, the BimC motif and adjacent C-terminal amino acids are particularly important for sliding force. In addition, moderate tail truncation increases midzone localization, but further truncation of residues N terminal to the BimC motif decreases midzone localization.

Actin–Microtubule Crosstalk Imparts Stiffness to the Contractile Ring in Fission Yeast

Actin–microtubule interactions are critical for cell division, yet how these networks of polymers mutually influence their mechanical properties and functions in live cells remains unknown. In fission yeast, the post-anaphase array (PAA) of microtubules assembles in the plane of the contractile ring, and its assembly relies on the Myp2p-dependent recruitment of Mto1p, a component of equatorial microtubule organizing centers (eMTOCs). The general organization of this array of microtubules and the impact on their physical attachment to the contractile ring remain unclear. We found that Myp2p facilitates the recruitment of Mto1p to the inner face of the contractile ring, where the eMTOCs polymerize microtubules without their direct interaction. The PAA microtubules form a dynamic polygon of Ase1p crosslinked microtubules inside the contractile ring. The specific loss of PAA microtubules affects the mechanical properties of the contractile ring of actin by lowering its stiffness. This change in the mechanical properties of the ring has no measurable impact on cytokinesis or on the anchoring of the ring. Our work proposes that the PAA microtubules exploit the contractile ring for their assembly and function during cell division, while the contractile ring may receive no benefit from these interactions.

The kinesin-5 protein Cut7 moves bidirectionally on fission yeast spindles with activity that increases in anaphase

Kinesin-5 motors are essential to separate mitotic spindle poles and assemble a bipolar spindle in many organisms. These motors crosslink and slide apart antiparallel microtubules via microtubule plus-end-directed motility. However, kinesin-5 localization is enhanced away from antiparallel overlaps. Increasing evidence suggests this localization occurs due to bidirectional motility or trafficking. The purified fission-yeast kinesin-5 protein Cut7 moves bidirectionally, but bidirectionality has not been shown in cells, and the function of the minus-end-directed movement is unknown. Here, we characterized the motility of Cut7 on bipolar and monopolar spindles and observed movement toward both plus- and minus-ends of microtubules. Notably, the activity of the motor increased at anaphase B onset. Perturbations to microtubule dynamics only modestly changed Cut7 movement, whereas Cut7 mutation reduced movement. These results suggest that the directed motility of Cut7 contributes to the movement of the motor. Comparison of the Cut7 mutant and human Eg5 (also known as KIF11) localization suggest a new hypothesis for the function of minus-end-directed motility and spindle-pole localization of kinesin-5s.

Ultrastructure expansion microscopy reveals the cellular architecture of budding and fission yeast

The budding and fission yeasts Saccharomyces cerevisiae and Schizosaccharomyces pombe have served as invaluable model organisms to study conserved fundamental cellular processes. Although super-resolution microscopy has in recent years paved the way to a better understanding of the spatial organization of molecules in cells, its wide use in yeasts has remained limited due to the specific know-how and instrumentation required, contrasted with the relative ease of endogenous tagging and live-cell fluorescence microscopy. To facilitate super-resolution microscopy in yeasts, we have extended the ultrastructure expansion microscopy (U-ExM) method to both S. cerevisiae and S. pombe, enabling a 4-fold isotropic expansion. We demonstrate that U-ExM allows imaging of the microtubule cytoskeleton and its associated spindle pole body, notably unveiling the Sfi1p–Cdc31p spatial organization on the appendage bridge structure. In S. pombe, we validate the method by monitoring the homeostatic regulation of nuclear pore complex number through the cell cycle. Combined with NHS-ester pan-labelling, which provides a global cellular context, U-ExM reveals the subcellular organization of these two yeast models and provides a powerful new method to augment the already extensive yeast toolbox.

This article has an associated First Person interview with Kerstin Hinterndorfer and Felix Mikus, two of the joint first authors of the paper.

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.

Oxidative stress induces meiotic defects of oocytes in a mouse psoriasis model

Psoriasis, an immune-mediated inflammatory disease, is associated with poor pregnancy outcomes. Emerging evidence indicates that these defects are likely attributed to compromised oocyte competence. Nevertheless, little is known about the underlying associated mechanisms between psoriasis and poor oocyte quality. In this study, we construct an imiquimod-induced chronic psoriasis-like mouse model to review the effects of psoriasis on oocyte quality. We discover that oocytes from psoriasis-like mice display spindle/chromosome disorganization, kinetochore-microtubule mis-attachment, and aneuploidy. Importantly, our results show that melatonin supplement in vitro and in vivo not only increases the rate of matured oocytes but also significantly attenuates oxidative stress and meiotic defects by restoring mitochondrial function in oocytes from psoriasis-like mice. Altogether, our data uncover the adverse effects of psoriasis symptoms on oocytes, and melatonin supplement ameliorates oxidative stress and meiotic defects of oocytes from psoriatic mice.

Microtubule rescue at midzone edges promotes overlap stability and prevents spindle collapse during anaphase B

During anaphase B, molecular motors slide interpolar microtubules to elongate the mitotic spindle, contributing to the separation of chromosomes. However, sliding of antiparallel microtubules reduces their overlap, which may lead to spindle breakage, unless microtubules grow to compensate sliding. How sliding and growth are coordinated is still poorly understood. In this study, we have used the fission yeast S. pombe to measure microtubule dynamics during anaphase B. We report that the coordination of microtubule growth and sliding relies on promoting rescues at the midzone edges. This makes microtubules stable from pole to midzone, while their distal parts including the plus ends alternate between assembly and disassembly. Consequently, the midzone keeps a constant length throughout anaphase, enabling sustained sliding without the need for a precise regulation of microtubule growth speed. Additionally, we found that in S. pombe, which undergoes closed mitosis, microtubule growth speed decreases when the nuclear membrane wraps around the spindle midzone.

Anaphase B: Long-standing models meet new concepts

Mitotic cell divisions ensure stable transmission of genetic information from a mother to daughter cells in a series of generations. To ensure this crucial task is accomplished, the cell forms a bipolar structure called the mitotic spindle that divides sister chromatids to the opposite sides of the dividing mother cell. After successful establishment of stable attachments of microtubules to chromosomes and inspection of connections between them, at the heart of mitosis, the cell starts the process of segregation. This spectacular moment in the life of a cell is termed anaphase, and it involves two distinct processes: depolymerization of microtubules bound to chromosomes, which is also known as anaphase A, and elongation of the spindle or anaphase B. Both processes ensure physical separation of disjointed sister chromatids. In this chapter, we review the mechanisms of anaphase B spindle elongation primarily in mammalian systems, combining different pioneering ideas and concepts with more recent findings that shed new light on the force generation and regulation of biochemical modules operating during spindle elongation. Finally, we present a comprehensive model of spindle elongation that includes structural, biophysical, and molecular aspects of anaphase B.

Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator

Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.

Modeling reveals cortical dynein-dependent fluctuations in bipolar spindle length

Proper formation and maintenance of the mitotic spindle is required for faithful cell division. Although much work has been done to understand the roles of the key molecular components of the mitotic spindle, identifying the consequences of force perturbations in the spindle remains a challenge. We develop a computational framework accounting for the minimal force requirements of mitotic progression. To reflect early spindle formation, we model microtubule dynamics and interactions with major force-generating motors, excluding chromosome interactions that dominate later in mitosis. We directly integrate our experimental data to define and validate the model. We then use simulations to analyze individual force components over time and their relationship to spindle dynamics, making it distinct from previously published models. We show through both model predictions and biological manipulation that rather than achieving and maintaining a constant bipolar spindle length, fluctuations in pole-to-pole distance occur that coincide with microtubule binding and force generation by cortical dynein. Our model further predicts that high dynein activity is required for spindle bipolarity when kinesin-14 (HSET) activity is also high. To the best of our knowledge, our results provide novel insight into the role of cortical dynein in the regulation of spindle bipolarity.

Kinesin-6 Klp9 orchestrates spindle elongation by regulating microtubule sliding and growth

Mitotic spindle function depends on the precise regulation of microtubule dynamics and microtubule sliding. Throughout mitosis, both processes have to be orchestrated to establish and maintain spindle stability. We show that during anaphase B spindle elongation in Schizosaccharomyces pombe, the sliding motor Klp9 (kinesin-6) also promotes microtubule growth in vivo. In vitro, Klp9 can enhance and dampen microtubule growth, depending on the tubulin concentration. This indicates that the motor is able to promote and block tubulin subunit incorporation into the microtubule lattice in order to set a well-defined microtubule growth velocity. Moreover, Klp9 recruitment to spindle microtubules is dependent on its dephosphorylation mediated by XMAP215/Dis1, a microtubule polymerase, creating a link between the regulation of spindle length and spindle elongation velocity. Collectively, we unravel the mechanism of anaphase B, from Klp9 recruitment to the motors dual-function in regulating microtubule sliding and microtubule growth, allowing an inherent coordination of both processes.

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.

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.

The phosphatase inhibitor Sds23 promotes symmetric spindle positioning in fission yeast

A hallmark of cell division in eukaryotic cells is the formation and elongation of a microtubule (MT)-based mitotic spindle. Proper positioning of the spindle is critical to ensure equal segregation of the genetic material to the resulting daughter cells. Both the timing of spindle elongation and constriction of the actomyosin contractile ring must be precisely coordinated to prevent missegregation or damage to the genetic material during cellular division. Here, we show that Sds23, an inhibitor of protein phosphatases, contributes to proper positioning of elongating spindles in fission yeast cells. We found that sds23∆ mutant cells exhibit asymmetric spindles that initially elongate asymmetrically toward one end of the dividing cell. Spindle asymmetry in sds23∆ cells results from a defect that is distinct from previously identified mechanisms, including MT protrusions and enlarged vacuoles. Combined with our previous work, this study demonstrates that Sds23, an inhibitor of PP2A-family protein phosphatases, promotes proper positioning of both the bipolar spindle and cytokinetic ring during fission yeast cell division. These two steps ensure the overall symmetry and fidelity of the cell division process.

Closed mitosis requires local disassembly of the nuclear envelope

At the end of mitosis, eukaryotic cells must segregate the two copies of their replicated genome into two new nuclear compartments1. They do this either by first dismantling and later reassembling the nuclear envelope in an 'open mitosis' or by reshaping an intact nucleus and then dividing it into two in a 'closed mitosis'2,3. Mitosis has been studied in a wide variety of eukaryotes for more than a century4, but how the double membrane of the nuclear envelope is split into two at the end of a closed mitosis without compromising the impermeability of the nuclear compartment remains unknown5. Here, using the fission yeast Schizosaccharomyces pombe (a classical model for closed mitosis5), genetics, live-cell imaging and electron tomography, we show that nuclear fission is achieved via local disassembly of nuclear pores within the narrow bridge that links segregating daughter nuclei. In doing so, we identify the protein Les1, which is localized to the inner nuclear envelope and restricts the process of local nuclear envelope breakdown to the bridge midzone to prevent the leakage of material from daughter nuclei. The mechanism of local nuclear envelope breakdown in a closed mitosis therefore closely mirrors nuclear envelope breakdown in open mitosis3, revealing an unexpectedly high conservation of nuclear remodelling mechanisms across diverse eukaryotes.

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.

Three-dimensional organization of the cytoskeleton: A cryo-electron tomography perspective

Traditionally, structures of cytoskeletal components have been studied ex situ, that is, with biochemically purified materials. There are compelling reasons to develop approaches to study them in situ in their native functional context. In recent years, cryo-electron tomography emerged as a powerful method for visualizing the molecular organization of unperturbed cellular landscapes with the potential to attain near-atomic resolution. Here, we review recent works on the cytoskeleton using cryo-electron tomography, demonstrating the power of in situ studies. We also highlight the potential of this method in addressing important questions pertinent to the field of cytoskeletal biomechanics.

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.

Before a cell divides, it must make a copy of its genetic material and then promptly split in two. This process, called mitosis, is coordinated by many different molecular machines. The DNA is copied, then the duplicated chromosomes line up at the middle of the cell. Next, an apparatus called the mitotic spindle latches onto the chromosomes before pulling them apart. The mitotic spindle is a bundle of long, thin filaments called microtubules. It attaches to chromosomes at the kinetochore, the point where two copied chromosomes are cinched together in their middle.

Proper cell division is vital for the healthy growth of all organisms, big and small, and yet some parts of the process remain poorly understood despite extensive study. Specifically, there is more to learn about how the mitotic spindle self-assembles, and how microtubules and kinetochores work together to correctly orient and segregate chromosomes into two sister cells. These nanoscale processes are happening a hundred times a minute, so computer simulations are a good way to test what we know.

Edelmaier et al. developed a computer model to simulate cell division in fission yeast, a species of yeast often used to study fundamental processes in the cell. The model simulates how the mitotic spindle assembles, how its microtubules attach to the kinetochore and the force required to pull two sister chromosomes apart. Building the simulation involved modelling interactions between the mitotic spindle and kinetochore, their movement and forces applied. To test its accuracy, model simulations were compared to recordings of the mitotic spindle – including its length, structure and position – imaged from dividing yeast cells.

Running the simulation, Edelmaier et al. found that several key effects are essential for the proper movement of chromosomes in mitosis. This includes holding chromosomes in the correct orientation as the mitotic spindle assembles and controlling the relative position of microtubules as they attach to the kinetochore. Misaligned attachments must also be readily deconstructed and corrected to prevent any errors. The simulations also showed that kinetochores must begin to exert more force (to separate the chromosomes) once the mitotic spindle is attached correctly.

Altogether, these findings improve the current understanding of how the mitotic spindle and its counterparts control cell division. Errors in chromosome segregation are associated with birth defects and cancer in humans, and this new simulation could potentially now be used to help make predictions about how to correct mistakes in the process.

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.

Microtubule number and length determine cellular shape and function in Plasmodium

Microtubules are cytoskeletal filaments essential for many cellular processes, including establishment and maintenance of polarity, intracellular transport, division and migration. In most metazoan cells, the number and length of microtubules are highly variable, while they can be precisely defined in some protozoan organisms. However, in either case the significance of these two key parameters for cells is not known. Here, we quantitatively studied the impact of modulating microtubule number and length in Plasmodium, the protozoan parasite causing malaria. Using a gene deletion and replacement strategy targeting one out of two α-tubulin genes, we show that chromosome segregation proceeds in the oocysts even in the absence of microtubules. However, fewer and shorter microtubules severely impaired the formation, motility and infectivity of Plasmodium sporozoites, the forms transmitted by the mosquito, which usually contain 16 microtubules. We found that α-tubulin expression levels directly determined the number of microtubules, suggesting a high nucleation barrier as supported by a mathematical model. Infectious sporozoites were only formed in parasite lines featuring at least 10 microtubules, while parasites with 9 or fewer microtubules failed to transmit.

Pivot-and-bond model explains microtubule bundle formation

During mitosis, microtubules form a spindle, which is responsible for proper segregation of the genetic material. A common structural element in a mitotic spindle is a parallel bundle, consisting of two or more microtubules growing from the same origin and held together by cross-linking proteins. An interesting question is what are the physical principles underlying the formation and stability of such microtubule bundles. Here we show, by introducing the pivot-and-bond model, that random angular movement of microtubules around the spindle pole and forces exerted by cross-linking proteins can explain the formation of microtubule bundles as observed in our experiments. The model predicts that stable parallel bundles can form in the presence of either passive crosslinkers or plus-end directed motors, but not minus-end directed motors. In the cases where bundles form, the time needed for their formation depends mainly on the concentration of cross-linking proteins and the angular diffusion of the microtubule. In conclusion, the angular motion drives the alignment of microtubules, which in turn allows the cross-linking proteins to connect the microtubules into a stable bundle.

Theory of Cytoskeletal Reorganization during Cross-Linker-Mediated Mitotic Spindle Assembly

Cells grow, move, and respond to outside stimuli by large-scale cytoskeletal reorganization. A prototypical example of cytoskeletal remodeling is mitotic spindle assembly, during which microtubules nucleate, undergo dynamic instability, bundle, and organize into a bipolar spindle. Key mechanisms of this process include regulated filament polymerization, cross-linking, and motor-protein activity. Remarkably, using passive cross-linkers, fission yeast can assemble a bipolar spindle in the absence of motor proteins. We develop a torque-balance model that describes this reorganization because of dynamic microtubule bundles, spindle-pole bodies, the nuclear envelope, and passive cross-linkers to predict spindle-assembly dynamics. We compare these results to those obtained with kinetic Monte Carlo-Brownian dynamics simulations, which include cross-linker-binding kinetics and other stochastic effects. Our results show that rapid cross-linker reorganization to microtubule overlaps facilitates cross-linker-driven spindle assembly, a testable prediction for future experiments. Combining these two modeling techniques, we illustrate a general method for studying cytoskeletal network reorganization.

Quantifying Tubulin Concentration and Microtubule Number Throughout the Fission Yeast Cell Cycle

The fission yeast Schizosaccharomyces pombe serves as a good genetic model organism for the molecular dissection of the microtubule (MT) cytoskeleton. However, analysis of the number and distribution of individual MTs throughout the cell cycle, particularly during mitosis, in living cells is still lacking, making quantitative modelling imprecise. We use quantitative fluorescent imaging and analysis to measure the changes in tubulin concentration and MT number and distribution throughout the cell cycle at a single MT resolution in living cells. In the wild-type cell, both mother and daughter spindle pole body (SPB) nucleate a maximum of 23 ± 6 MTs at the onset of mitosis, which decreases to a minimum of 4 ± 1 MTs at spindle break down. Interphase MT bundles, astral MT bundles, and the post anaphase array (PAA) microtubules are composed primarily of 1 ± 1 individual MT along their lengths. We measure the cellular concentration of αβ-tubulin subunits to be ~5 µM throughout the cell cycle, of which one-third is in polymer form during interphase and one-quarter is in polymer form during mitosis. This analysis provides a definitive characterization of αβ-tubulin concentration and MT number and distribution in fission yeast and establishes a foundation for future quantitative comparison of mutants defective in MTs.

Kinesin-6 regulates cell-size-dependent spindle elongation velocity to keep mitosis duration constant in fission yeast

The length of the mitotic spindle scales with cell size in a wide range of organisms during embryonic development. Interestingly, in C. elegans embryos, this goes along with temporal regulation: larger cells speed up spindle assembly and elongation. We demonstrate that, similarly in fission yeast, spindle length and spindle dynamics adjust to cell size, which allows to keep mitosis duration constant. Since prolongation of mitosis was shown to affect cell viability, this may resemble a mechanism to regulate mitosis duration. We further reveal how the velocity of spindle elongation is regulated: coupled to cell size, the amount of kinesin-6 Klp9 molecules increases, resulting in an acceleration of spindle elongation in anaphase B. In addition, the number of Klp9 binding sites to microtubules increases overproportionally to Klp9 molecules, suggesting that molecular crowding inversely correlates to cell size and might have an impact on spindle elongation velocity control.

Elastic strain and twist analysis of protein structural data and allostery of the transmembrane channel KcsA

The abundance of available static protein structural data makes the more effective analysis and interpretation of this data a valuable tool to supplement the experimental study of protein mechanics. Structural displacements can be difficult to analyze and interpret. Previously, we showed that strains provide a more natural and interpretable representation of protein deformations, revealing mechanical coupling between spatially distinct sites of allosteric proteins. Here, we demonstrate that other transformations of displacements yield additional insights. We calculate the divergence and curl of deformations of the transmembrane channel KcsA. Additionally, we introduce quantities analogous to bend, splay, and twist deformation energies of nematic liquid crystals. These transformations enable the decomposition of displacements into different modes of deformation, helping to characterize the type of deformation a protein undergoes. We apply these calculations to study the filter and gating regions of KcsA. We observe a continuous path of rotational deformations physically coupling these two regions, and, we propose, underlying the allosteric interaction between these regions. Bend, splay, and twist distinguish KcsA gate opening, filter opening, and filter-gate coupling, respectively. In general, physically meaningful representations of deformations (like strain, curl, bend, splay, and twist) can make testable predictions and yield insights into protein mechanics, augmenting experimental methods and more fully exploiting available structural data.

Structural and functional differences between porcine brain and budding yeast microtubules

The cytoskeleton of eukaryotic cells relies on microtubules to perform many essential functions. We have previously shown that, in spite of the overall conservation in sequence and structure of tubulin subunits across species, there are differences between mammalian and budding yeast microtubules with likely functional consequences for the cell. Here we expand our structural and function comparison of yeast and porcine microtubules to show different distribution of protofilament number in microtubules assembled in vitro from these two species. The different geometry at lateral contacts between protofilaments is likely due to a more polar interface in yeast. We also find that yeast tubulin forms longer and less curved oligomers in solution, suggesting stronger tubulin:tubulin interactions along the protofilament. Finally, we observed species-specific plus-end tracking activity for EB proteins: yeast Bim1 tracked yeast but not mammalian MTs, and human EB1 tracked mammalian but not yeast MTs. These findings further demonstrate that subtle sequence differences in tubulin sequence can have significant structural and functional consequences in microtubule structure and behavior.

Structural differences between yeast and mammalian microtubules revealed by cryo-EM

Yeast MTs do not appear to undergo the lattice compaction seen in mammalian MTs upon GTP hydrolysis. Binding of the +TIP Bim1, both between and within αβ-tubulin dimers, causes compaction of yeast MTs and their rapid disassembly.

Microtubules are polymers of αβ-tubulin heterodimers essential for all eukaryotes. Despite sequence conservation, there are significant structural differences between microtubules assembled in vitro from mammalian or budding yeast tubulin. Yeast MTs were not observed to undergo compaction at the interdimer interface as seen for mammalian microtubules upon GTP hydrolysis. Lack of compaction might reflect slower GTP hydrolysis or a different degree of allosteric coupling in the lattice. The microtubule plus end–tracking protein Bim1 binds yeast microtubules both between αβ-tubulin heterodimers, as seen for other organisms, and within tubulin dimers, but binds mammalian tubulin only at interdimer contacts. At the concentrations used in cryo-electron microscopy, Bim1 causes the compaction of yeast microtubules and induces their rapid disassembly. Our studies demonstrate structural differences between yeast and mammalian microtubules that likely underlie their differing polymerization dynamics. These differences may reflect adaptations to the demands of different cell size or range of physiological growth temperatures.

Balance of microtubule stiffness and cortical tension determines the size of blood cells with marginal band across species

The fast bloodstream of animals is associated with large shear stresses. To withstand these conditions, blood cells have evolved a special morphology and a specific internal architecture to maintain their integrity over several weeks. For instance, nonmammalian red blood cells, mammalian erythroblasts, and platelets have a peripheral ring of microtubules, called the marginal band, that flattens the overall cell morphology by pushing on the cell cortex. In this work, we model how the shape of these cells stems from the balance between marginal band rigidity and cortical tension. We predict that the diameter of the cell scales with the total microtubule polymer and verify the predicted law across a wide range of species. Our analysis also shows that the combination of the marginal band rigidity and cortical tension increases the ability of the cell to withstand forces without deformation. Finally, we model the marginal band coiling that occurs during the disk-to-sphere transition observed, for instance, at the onset of blood platelet activation. We show that when cortical tension increases faster than cross-linkers can unbind, the marginal band will coil, whereas if the tension increases more slowly, the marginal band may shorten as microtubules slide relative to each other.

Physical determinants of bipolar mitotic spindle assembly and stability in fission yeast

Mitotic spindles use an elegant bipolar architecture to segregate duplicated chromosomes with high fidelity. Bipolar spindles form from a monopolar initial condition; this is the most fundamental construction problem that the spindle must solve. Microtubules, motors, and cross-linkers are important for bipolarity, but the mechanisms necessary and sufficient for spindle assembly remain unknown. We describe a physical model that exhibits de novo bipolar spindle formation. We began with physical properties of fission-yeast spindle pole body size and microtubule number, kinesin-5 motors, kinesin-14 motors, and passive cross-linkers. Our model results agree quantitatively with our experiments in fission yeast, thereby establishing a minimal system with which to interrogate collective self-assembly. By varying the features of our model, we identify a set of functions essential for the generation and stability of spindle bipolarity. When kinesin-5 motors are present, their bidirectionality is essential, but spindles can form in the presence of passive cross-linkers alone. We also identify characteristic failed states of spindle assembly-the persistent monopole, X spindle, separated asters, and short spindle, which are avoided by the creation and maintenance of antiparallel microtubule overlaps. Our model can guide the identification of new, multifaceted strategies to induce mitotic catastrophes; these would constitute novel strategies for cancer chemotherapy.

Anaphase B

Anaphase B spindle elongation is characterized by the sliding apart of overlapping antiparallel interpolar (ip) microtubules (MTs) as the two opposite spindle poles separate, pulling along disjoined sister chromatids, thereby contributing to chromosome segregation and the propagation of all cellular life. The major biochemical “modules” that cooperate to mediate pole–pole separation include: (i) midzone pushing or (ii) braking by MT crosslinkers, such as kinesin-5 motors, which facilitate or restrict the outward sliding of antiparallel interpolar MTs (ipMTs); (iii) cortical pulling by disassembling astral MTs (aMTs) and/or dynein motors that pull aMTs outwards; (iv) ipMT plus end dynamics, notably net polymerization; and (v) ipMT minus end depolymerization manifest as poleward flux. The differential combination of these modules in different cell types produces diversity in the anaphase B mechanism. Combinations of antagonist modules can create a force balance that maintains the dynamic pre-anaphase B spindle at constant length. Tipping such a force balance at anaphase B onset can initiate and control the rate of spindle elongation. The activities of the basic motor filament components of the anaphase B machinery are controlled by a network of non-motor MT-associated proteins (MAPs), for example the key MT cross-linker, Ase1p/PRC1, and various cell-cycle kinases, phosphatases, and proteases. This review focuses on the molecular mechanisms of anaphase B spindle elongation in eukaryotic cells and briefly mentions bacterial DNA segregation systems that operate by spindle elongation.

Near-atomic cryo-EM structure of PRC1 bound to the microtubule

Proteins that associate with microtubules (MTs) are crucial to generate MT arrays and establish different cellular architectures. One example is PRC1 (protein regulator of cytokinesis 1), which cross-links antiparallel MTs and is essential for the completion of mitosis and cytokinesis. Here we describe a 4-Å-resolution cryo-EM structure of monomeric PRC1 bound to MTs. Residues in the spectrin domain of PRC1 contacting the MT are highly conserved and interact with the same pocket recognized by kinesin. We additionally found that PRC1 promotes MT assembly even in the presence of the MT stabilizer taxol. Interestingly, the angle of the spectrin domain on the MT surface corresponds to the previously observed cross-bridge angle between MTs cross-linked by full-length, dimeric PRC1. This finding, together with molecular dynamic simulations describing the intrinsic flexibility of PRC1, suggests that the MT-spectrin domain interface determines the geometry of the MT arrays cross-linked by PRC1.

Centrosome centering and decentering by microtubule network rearrangement

Numerical simulations are used to investigate the role of microtubule network architecture in centrosome positioning. Microtubule gliding along cell edges and pivoting around the centrosome are key regulators of the orientation of pushing forces, the magnitude of which depends on the number, dynamics, and stiffness of microtubules.

The centrosome is positioned at the cell center by pushing and pulling forces transmitted by microtubules (MTs). Centrosome decentering is often considered to result from asymmetric, cortical pulling forces exerted in particular by molecular motors on MTs and controlled by external cues affecting the cell cortex locally. Here we used numerical simulations to investigate the possibility that it could equally result from the redistribution of pushing forces due to a reorientation of MTs. We first showed that MT gliding along cell edges and pivoting around the centrosome regulate MT rearrangement and thereby direct the spatial distribution of pushing forces, whereas the number, dynamics, and stiffness of MTs determine the magnitude of these forces. By modulating these parameters, we identified different regimes, involving both pushing and pulling forces, characterized by robust centrosome centering, robust off-centering, or “reactive” positioning. In the last-named conditions, weak asymmetric cues can induce a misbalance of pushing and pulling forces, resulting in an abrupt transition from a centered to an off-centered position. Taken together, these results point to the central role played by the configuration of the MTs on the distribution of pushing forces that position the centrosome. We suggest that asymmetric external cues should not be seen as direct driver of centrosome decentering and cell polarization but instead as inducers of an effective reorganization of the MT network, fostering centrosome motion to the cell periphery.

Amplification of actin polymerization forces

The actin cytoskeleton drives many essential processes in vivo, using molecular motors and actin assembly as force generators. We discuss here the propagation of forces caused by actin polymerization, highlighting simple configurations where the force developed by the network can exceed the sum of the polymerization forces from all filaments.

Force Generation by Molecular-Motor-Powered Microtubule Bundles; Implications for Neuronal Polarization and Growth

The heavily cross-linked microtubule (MT) bundles found in neuronal processes play a central role in the initiation, growth and maturation of axons and dendrites; however, a quantitative understanding of their mechanical function is still lacking. We here developed computer simulations to investigate the dynamics of force generation in 1D bundles of MTs that are cross-linked and powered by molecular motors. The motion of filaments and the forces they exert are investigated as a function of the motor type (unipolar or bipolar), MT density and length, applied load, and motor connectivity. We demonstrate that only unipolar motors (e.g., kinesin-1) can provide the driving force for bundle expansion, while bipolar motors (e.g., kinesin-5) oppose it. The force generation capacity of the bundles is shown to depend sharply on the fraction of unipolar motors due to a percolation transition that must occur in the bundle. Scaling laws between bundle length, force, MT length and motor fraction are presented. In addition, we investigate the dynamics of growth in the presence of a constant influx of MTs. Beyond a short equilibration period, the bundles grow linearly in time. In this growth regime, the bundle extends as one mass forward with most filaments sliding with the growth velocity. The growth velocity is shown to be dictated by the inward flux of MTs, to inversely scale with the load and to be independent of the free velocity of the motors. These findings provide important molecular-level insights into the mechanical function of the MT cytoskeleton in normal axon growth and regeneration after injury.

The mesh is a network of microtubule connectors that stabilizes individual kinetochore fibers of the mitotic spindle

Kinetochore fibers (K-fibers) of the mitotic spindle are force-generating units that power chromosome movement during mitosis. K-fibers are composed of many microtubules that are held together throughout their length. Here, we show, using 3D electron microscopy, that K-fiber microtubules (MTs) are connected by a network of MT connectors. We term this network ‘the mesh’. The K-fiber mesh is made of linked multipolar connectors. Each connector has up to four struts, so that a single connector can link up to four MTs. Molecular manipulation of the mesh by overexpression of TACC3 causes disorganization of the K-fiber MTs. Optimal stabilization of K-fibers by the mesh is required for normal progression through mitosis. We propose that the mesh stabilizes K-fibers by pulling MTs together and thereby maintaining the integrity of the fiber. Our work thus identifies the K-fiber meshwork of linked multipolar connectors as a key integrator and determinant of K-fiber structure and function.

DOI:http://dx.doi.org/10.7554/eLife.07635.001

Before a cell divides, its genetic material must be copied and then equally distributed between the newly formed daughter cells. In the cells of plants, animals, and fungi, a structure known as the spindle pulls the two copies of the chromosomes apart. The spindle is made up of a network of long, protein filaments called microtubules, and the bundles of microtubules that attach to the chromosomes are referred to as ‘K-fibers’.

K-fibers are organized in a way that provides strength. These bundles of microtubules are held together throughout their entire length and, in 2011, it was suggested that a group of proteins including one called TACC3 could cross-link adjacent microtubules within K-fibers. However, it remained unclear how these proteins achieved this.

Now, Nixon et al.—including several of the researchers involved in the 2011 work—have used a technique called 3D electron tomography to analyze what holds the K-fibers together in human cells. This analysis revealed struts or connectors that hold together adjacent microtubules within K-fibers. These connectors can vary in size and a single connector can link up to four microtubules. This means that, in a three-dimensional view, the connectors appear as a ‘mesh’ between the microtubules in the bundle.

Nixon et al. then increased the levels of the TACC3 protein and found that the K-fibers became disorganized. The spacing of the microtubules with the K-fibers was reduced so that they were more tightly packed than normal. These observations suggest that ‘the mesh’ influences the microtubule spacing within a K-fiber.

Nixon et al. analyzed how disorganized K-fibers affected dividing cells and found that it took longer for the chromosomes to move to the newly forming daughter cells. This suggests that cells must maintain optimal levels of TACC3 to ensure that the K-fibers can effectively separate the chromosomes. Further work is needed to identify the other proteins and molecules that make up the mesh.

DOI:http://dx.doi.org/10.7554/eLife.07635.002