The Mitotic Spindle in the One-Cell C. elegans Embryo Is Positioned with High Precision and Stability

Relaxation and Noise-Driven Oscillations in a Model of Mitotic Spindle Dynamics

During cell division, the mitotic spindle moves dynamically through the cell to position the chromosomes and determine the ultimate spatial position of the two daughter cells. These movements have been attributed to the action of cortical force generators which pull on the astral microtubules to position the spindle, as well as pushing events by these same microtubules against the cell cortex and plasma membrane. Attachment and detachment of cortical force generators working antagonistically against centring forces of microtubules have been modelled previously (Grill et al. in Phys Rev Lett 94:108104, 2005) via stochastic simulations and mean-field Fokker-Planck equations (describing random motion of force generators) to predict oscillations of a spindle pole in one spatial dimension. Using systematic asymptotic methods, we reduce the Fokker-Planck system to a set of ordinary differential equations (ODEs), consistent with a set proposed by Grill et al., which can provide accurate predictions of the conditions for the Fokker-Planck system to exhibit oscillations. In the limit of small restoring forces, we derive an algebraic prediction of the amplitude of spindle-pole oscillations and demonstrate the relaxation structure of nonlinear oscillations. We also show how noise-induced oscillations can arise in stochastic simulations for conditions in which the mean-field Fokker-Planck system predicts stability, but for which the period can be estimated directly by the ODE model and the amplitude by a related stochastic differential equation that incorporates random binding kinetics.

A cytokinetic ring-driven cell rotation achieves Hertwig's rule in early development

Hertwig's rule states that cells divide along their longest axis, usually driven by forces acting on the mitotic spindle. Here, we show that in contrast to this rule, microtubule-based pulling forces in early Caenorhabditis elegans embryos align the spindle with the short axis of the cell. We combine theory with experiments to reveal that in order to correct this misalignment, inward forces generated by the constricting cytokinetic ring rotate the entire cell until the spindle is aligned with the cell's long axis. Experiments with slightly compressed mouse zygotes indicate that this cytokinetic ring-driven mechanism of ensuring Hertwig's rule is general for cells capable of rotating inside a confining shell, a scenario that applies to early cell divisions of many systems.

Cytoplasm mechanics and cellular organization

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

Lack of chromokinesin Klp-19 creates a more rigid midzone and affects force transmission during anaphase in C. elegans

Recent studies have highlighted the significance of the spindle midzone - the region positioned between chromosomes - in ensuring proper chromosome segregation. By combining advanced 3D electron tomography and cutting-edge light microscopy we have discovered a previously unknown role of the regulation of microtubule dynamics within the spindle midzone of C. elegans. Using Fluorescence recovery after photobleaching and a combination of second harmonic generation and two-photon fluorescence microscopy, we found that the length of the antiparallel microtubule overlap zone in the spindle midzone is constant throughout anaphase, and independent of cortical pulling forces as well as the presence of the microtubule bundling protein SPD-1. Further investigations of SPD-1 and the chromokinesin KLP-19 in C. elegans suggest that KLP-19 regulates the overlap length and functions independently of SPD-1. Our data shows that KLP-19 plays an active role in regulating the length and turn-over of microtubules within the midzone as well as the size of the antiparallel overlap region throughout mitosis. Depletion of KLP-19 in mitosis leads to an increase in microtubule length in the spindle midzone, which also leads to increased microtubule - microtubule interaction, thus building up a more robust microtubule network. The spindle is globally stiffer and more stable, which has implications for the transmission of forces within the spindle affecting chromosome segregation dynamics. Our data shows that by localizing KLP-19 to the spindle midzone in anaphase microtubule dynamics can be locally controlled allowing the formation of a functional midzone.

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

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

Stochastic model of T Cell repolarization during target elimination (II)

Cytotoxic T lymphocytes (T cells) and natural killer cells form a tight contact, the immunological synapse (IS), with target cells, where they release their lytic granules containing perforin/granzyme and cytokine-containing vesicles. During this process the cell repolarizes and moves the microtubule organizing center (MTOC) toward the IS. In the first part of our work we developed a computational model for the molecular-motor-driven motion of the microtubule cytoskeleton during T cell polarization and analyzed the effects of cortical-sliding and capture-shrinkage mechanisms. Here we use this model to analyze the dynamics of the MTOC repositioning in situations in which 1) the IS is in an arbitrary position with respect to the initial position of the MTOC and 2) the T cell has two IS at two arbitrary positions. In the case of one IS, we found that the initial position determines which mechanism is dominant and that the time of repositioning does not rise monotonously with the MTOC-IS distance. In the case of two IS, we observe several scenarios that have also been reported experimentally: the MTOC alternates stochastically (but with a well-defined average transition time) between the two IS; it wiggles in between the two IS without transiting to one of the two; or it is at some point pulled to one of the two IS and stays there. Our model allows one to predict which scenario emerges in dependency of the mechanisms in action and the number of dyneins present. We report that the presence of capture-shrinkage mechanism in at least one IS is necessary to assure the transitions in every cell configuration. Moreover, the frequency of transitions does not decrease with the distance between the two IS and is the highest when both mechanisms are present in both IS.

Astral microtubule cross-linking safeguards uniform nuclear distribution in the Drosophila syncytium

The early insect embryo develops as a multinucleated cell distributing the genome uniformly to the cell cortex. Mechanistic insight for nuclear positioning beyond cytoskeletal requirements is missing. Contemporary hypotheses propose actomyosin-driven cytoplasmic movement transporting nuclei or repulsion of neighbor nuclei driven by microtubule motors. Here, we show that microtubule cross-linking by Feo and Klp3A is essential for nuclear distribution and internuclear distance maintenance in Drosophila. Germline knockdown causes irregular, less-dense nuclear delivery to the cell cortex and smaller distribution in ex vivo embryo explants. A minimal internuclear distance is maintained in explants from control embryos but not from Feo-inhibited embryos, following micromanipulation-assisted repositioning. A dimerization-deficient Feo abolishes nuclear separation in embryo explants, while the full-length protein rescues the genetic knockdown. We conclude that Feo and Klp3A cross-linking of antiparallel microtubule overlap generates a length-regulated mechanical link between neighboring microtubule asters. Enabled by a novel experimental approach, our study illuminates an essential process of embryonic multicellularity.

Nuclear positioning during development: Pushing, pulling and flowing

The positioning of the nucleus, the central organelle of the cell, is an active and regulated process crucially linked to cell cycle, differentiation, migration, and polarity. Alterations in positioning have been correlated with cell and tissue function deficiency and genetic or chemical manipulation of nuclear position is embryonic lethal. Nuclear positioning is a precursor for symmetric or asymmetric cell division which is accompanied by fate determination of the daughter cells. Nuclear positioning also plays a key role during early embryonic developmental stages in insects, such as Drosophila, where hundreds of nuclei divide without cytokinesis and are distributed within the large syncytial embryo at roughly regular spacing. While the cytoskeletal elements and the linker proteins to the nucleus are fairly well characterised, including some of the force generating elements driving nuclear movement, there is considerable uncertainty about the biophysical mechanism of nuclear positioning, while the field is debating different force models. In this review, we highlight the current body of knowledge, discuss cell context dependent models of nuclear positioning, and outline open questions.

The coordination of spindle-positioning forces during the asymmetric division of the Caenorhabditis elegans zygote

In Caenorhabditis elegans zygote, astral microtubules generate forces essential to position the mitotic spindle, by pushing against and pulling from the cortex. Measuring microtubule dynamics there, we revealed the presence of two populations, corresponding to pulling and pushing events. It offers a unique opportunity to study, under physiological conditions, the variations of both spindle-positioning forces along space and time. We propose a threefold control of pulling force, by polarity, spindle position and mitotic progression. We showed that the sole anteroposterior asymmetry in dynein on-rate, encoding pulling force imbalance, is sufficient to cause posterior spindle displacement. The positional regulation, reflecting the number of microtubule contacts in the posterior-most region, reinforces this imbalance only in late anaphase. Furthermore, we exhibited the first direct proof that dynein processivity increases along mitosis. It reflects the temporal control of pulling forces, which strengthens at anaphase onset following mitotic progression and independently from chromatid separation. In contrast, the pushing force remains constant and symmetric and contributes to maintaining the spindle at the cell centre during metaphase.

The first steps in the life of a worm: Themes and variations in asymmetric division in C. elegans and other nematodes

Starting with Boveri in the 1870s, microscopic investigation of early embryogenesis in a broad swath of nematode species revealed the central role of asymmetric cell division in embryonic axis specification, blastomere positioning, and cell fate specification. Notably, across the class Chromadorea, a conserved theme emerges-asymmetry is first established in the zygote and specifies its asymmetric division, giving rise to an anterior somatic daughter cell and a posterior germline daughter cell. Beginning in the 1980s, the emergence of Caenorhabditis elegans as a model organism saw the advent of genetic tools that enabled rapid progress in our understanding of the molecular mechanisms underlying asymmetric division, in many cases defining key paradigms that turn out to regulate asymmetric division in a wide range of systems. Yet, the consequence of this focus on C. elegans came at the expense of exploring the extant diversity of developmental variation exhibited across nematode species. Given the resurgent interest in evolutionary studies facilitated in part by new tools, here we revisit the diversity in this asymmetric first division, juxtaposing molecular insight into mechanisms of symmetry-breaking, spindle positioning and fate specification, with a consideration of plasticity and variability within and between species. In the process, we hope to highlight questions of evolutionary forces and molecular variation that may have shaped the extant diversity of developmental mechanisms observed across Nematoda.

Two mechanisms drive pronuclear migration in mouse zygotes

A new life begins with the unification of the maternal and paternal chromosomes upon fertilization. The parental chromosomes first become enclosed in two separate pronuclei near the surface of the fertilized egg. The mechanisms that then move the pronuclei inwards for their unification are only poorly understood in mammals. Here, we report two mechanisms that act in concert to unite the parental genomes in fertilized mouse eggs. The male pronucleus assembles within the fertilization cone and is rapidly moved inwards by the flattening cone. Rab11a recruits the actin nucleation factors Spire and Formin-2 into the fertilization cone, where they locally nucleate actin and further accelerate the pronucleus inwards. In parallel, a dynamic network of microtubules assembles that slowly moves the male and female pronuclei towards the cell centre in a dynein-dependent manner. Both mechanisms are partially redundant and act in concert to unite the parental pronuclei in the zygote's centre.

CentTracker: a trainable, machine-learning-based tool for large-scale analyses of Caenorhabditis elegans germline stem cell mitosis

Investigating the complex interactions between stem cells and their native environment requires an efficient means to image them in situ. Caenorhabditis elegans germline stem cells (GSCs) are distinctly accessible for intravital imaging; however, long-term image acquisition and analysis of dividing GSCs can be technically challenging. Here we present a systematic investigation into the technical factors impacting GSC physiology during live imaging and provide an optimized method for monitoring GSC mitosis under minimally disruptive conditions. We describe CentTracker, an automated and generalizable image analysis tool that uses machine learning to pair mitotic centrosomes and that can extract a variety of mitotic parameters rapidly from large-scale data sets. We employ CentTracker to assess a range of mitotic features in a large GSC data set. We observe spatial clustering of mitoses within the germline tissue but no evidence that subpopulations with distinct mitotic profiles exist within the stem cell pool. We further find biases in GSC spindle orientation relative to the germline’s distal–proximal axis and thus the niche. The technical and analytical tools provided herein pave the way for large-scale screening studies of multiple mitotic processes in GSCs dividing in situ, in an intact tissue, in a living animal, under seemingly physiological conditions.

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

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

Positioning of the Centrosome and Golgi Complex

For over a century, the centrosome has been an organelle more easily tracked than understood, and the study of its peregrinations within the cell remains a chief underpinning of its functional investigation. Increasing attention and new approaches have been brought to bear on mechanisms that control centrosome localization in the context of cleavage plane determination, ciliogenesis, directional migration, and immunological synapse formation, among other cellular and developmental processes. The Golgi complex, often linked with the centrosome, presents a contrasting case of a pleiomorphic organelle for which functional studies advanced somewhat more rapidly than positional tracking. However, Golgi orientation and distribution has emerged as an area of considerable interest with respect to polarized cellular function. This chapter will review our current understanding of the mechanism and significance of the positioning of these organelles.

The polarity-induced force imbalance in Caenorhabditis elegans embryos is caused by asymmetric binding rates of dynein to the cortex

During asymmetric cell division, the molecular motor dynein generates cortical pulling forces that position the spindle to reflect polarity and adequately distribute cell fate determinants. In Caenorhabditis elegans embryos, despite a measured anteroposterior force imbalance, antibody staining failed to reveal dynein enrichment at the posterior cortex, suggesting a transient localization there. Dynein accumulates at the microtubule plus ends, in an EBP-2EB-dependent manner. This accumulation, although not transporting dynein, contributes modestly to cortical forces. Most dyneins may instead diffuse to the cortex. Tracking of cortical dynein revealed two motions: one directed and the other diffusive-like, corresponding to force-generating events. Surprisingly, while dynein is not polarized at the plus ends or in the cytoplasm, diffusive-like tracks were more frequently found at the embryo posterior tip, where the forces are higher. This asymmetry depends on GPR-1/2LGN and LIN-5NuMA, which are enriched there. In csnk-1(RNAi) embryos, the inverse distribution of these proteins coincides with an increased frequency of diffusive-like tracks anteriorly. Importantly, dynein cortical residence time is always symmetric. We propose that the dynein-binding rate at the posterior cortex is increased, causing the polarity-reflecting force imbalance. This mechanism of control supplements the regulation of mitotic progression through the nonpolarized dynein detachment rate.

Microtubule Feedback and LET-99-Dependent Control of Pulling Forces Ensure Robust Spindle Position

During asymmetric division of the Caenorhabditis elegans zygote, to properly distribute cell fate determinants, the mitotic spindle is asymmetrically localized by a combination of centering and cortical-pulling microtubule-mediated forces, the dynamics of the latter being regulated by mitotic progression. Here, we show a, to our knowledge, novel and additional regulation of these forces by spindle position itself. For that, we observed the onset of transverse spindle oscillations, which reflects the burst of anaphase pulling forces. After delaying anaphase onset, we found that the position at which the spindle starts to oscillate was unchanged compared to control embryos and uncorrelated to anaphase onset. In mapping the cortical microtubule dynamics, we measured a steep increase in microtubule contact density after the posterior centrosome reached the critical position of 70% of embryo length, strongly suggesting the presence of a positional switch for spindle oscillations. Expanding a previous model based on a force-generator temporal control, we implemented this positional switch and observed that the large increase in microtubule density accounted for the pulling force burst. Thus, we propose that the spindle position influences the cortical availability of microtubules on which the active force generators, controlled by cell cycle progression, can pull. Importantly, we found that this positional control relies on the polarity-dependent LET-99 cortical band, the boundary of which could be probed by microtubules. This dual positional and temporal control well accounted for our observation that the oscillation onset position resists changes in cellular geometry and moderate variations in the active force generator number. Finally, our model suggests that spindle position at mitosis end is more sensitive to the polarity factor LET-99, which restricts the region of active force generators to a posterior-most region, than to microtubule number or force generator number/activity. Overall, we show that robustness in spindle positioning originates in cell mechanics rather than biochemical networks.

Functions of actin in mouse oocytes at a glance

Gametes undergo a specialized and reductional cell division termed meiosis. Female gametes (oocytes) undergo two rounds of meiosis; the first meiotic division produces the fertilizable egg, while the second meiotic division occurs upon fertilization. Both meiotic divisions are highly asymmetric, producing a large egg and small polar bodies. Actin takes over various essential function during oocyte meiosis, many of which commonly rely on microtubules in mitotic cells. Specifically, the actin network has been linked to long-range vesicle transport, nuclear positioning, spindle migration and anchorage, polar body extrusion and accurate chromosome segregation in mammalian oocytes. In this Cell Science at a Glance article and the accompanying poster, we summarize the many functions of the actin cytoskeleton in oocytes, with a focus on findings from the mouse model system.

Physical Forces Determining the Persistency and Centering Precision of Microtubule Asters

In early embryos, microtubules form star-shaped aster structures that can measure up to hundreds of micrometres, and move at high speeds to find the geometrical centre of the cell. This process, known as aster centration, is essential for the fidelity of cell division and development, but how cells succeed in moving these large structures through their crowded and fluctuating cytoplasm remains unclear. Here, we demonstrate that the positional fluctuations of migrating sea urchin sperm asters are small, anisotropic, and associated with the stochasticity of dynein-dependent forces moving the aster. Using in vivo magnetic tweezers to directly measure aster forces inside cells, we derive a linear aster force-velocity relationship and provide evidence for a spring-like active mechanism stabilizing the transverse position of the asters. The large frictional coefficient and spring constant quantitatively account for the amplitude and growth characteristics of athermal positional fluctuations, demonstrating that aster mechanics ensure noise suppression to promote persistent and precise centration. These findings define generic biophysical regimes of active cytoskeletal mechanics underlying the accuracy of cell division and early embryonic development.

The preprophase band of microtubules controls the robustness of division orientation in plants

Controlling cell division plane orientation is essential for morphogenesis in multicellular organisms. In plant cells, the future cortical division plane is marked before mitotic entry by the preprophase band (PPB). Here, we characterized an Arabidopsis trm (TON1 Recruiting Motif) mutant that impairs PPB formation but does not affect interphase microtubules. Unexpectedly, PPB disruption neither abolished the capacity of root cells to define a cortical division zone nor induced aberrant cell division patterns but rather caused a loss of precision in cell division orientation. Our results advocate for a reassessment of PPB function and division plane determination in plants and show that a main output of this microtubule array is to limit spindle rotations in order to increase the robustness of cell division.

Physical Limits on the Precision of Mitotic Spindle Positioning by Microtubule Pushing forces: Mechanics of mitotic spindle positioning

Tissues are shaped and patterned by mechanical and chemical processes. A key mechanical process is the positioning of the mitotic spindle, which determines the size and location of the daughter cells within the tissue. Recent force and position-fluctuation measurements indicate that pushing forces, mediated by the polymerization of astral microtubules against- the cell cortex, maintain the mitotic spindle at the cell center in Caenorhabditis elegans embryos. The magnitude of the centering forces suggests that the physical limit on the accuracy and precision of this centering mechanism is determined by the number of pushing microtubules rather than by thermally driven fluctuations. In cells that divide asymmetrically, anti-centering, pulling forces generated by cortically located dyneins, in conjunction with microtubule depolymerization, oppose the pushing forces to drive spindle displacements away from the center. Thus, a balance of centering pushing forces and anti-centering pulling forces localize the mitotic spindles within dividing C. elegans cells.