Physical basis of large microtubule aster growth

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

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

Developmental Control of Cell Cycle and Signaling

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

Robust cytoplasmic partitioning by solving an intrinsic cytoskeletal instability

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

The positioning mechanics of microtubule asters in Drosophila embryo explants

Microtubule asters are essential in localizing the action of microtubules in processes including mitosis and organelle positioning. In large cells, such as the one-cell sea urchin embryo, aster dynamics are dominated by hydrodynamic pulling forces. However, in systems with more densely positioned nuclei such as the early Drosophila embryo, which packs around 6000 nuclei within the syncytium in a crystalline-like order, it is unclear what processes dominate aster dynamics. Here, we take advantage of a cell cycle regulation Drosophila mutant to generate embryos with multiple asters, independent from nuclei. We use an ex vivo assay to further simplify this biological system to explore the forces generated by and between asters. Through live imaging, drug and optical perturbations, and theoretical modeling, we demonstrate that these asters likely generate an effective pushing force over short distances.

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

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

Length Regulation Drives Self-Organization in Filament-Motor Mixtures

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

Dynein-dependent collection of membranes defines the architecture and position of microtubule asters in isolated, geometrically confined volumes of cell-free extracts

It is well established that changes in the underlying architecture of the cell's microtubule network can affect organelle organization within the cytoplasm, but it remains unclear whether the spatial arrangement of organelles reciprocally influences the microtubule network. Here we use a combination of cell-free extracts and hydrogel microenclosures to characterize the relationship between membranes and microtubules during microtubule aster centration. We found that initially disperse ER membranes are collected by the aster and compacted near its nucleating center, all while the whole ensemble moves toward the geometric center of its confining enclosure. Once there, aster microtubules adopt a bullseye pattern with a high density annular ring of microtubules surrounding the compacted membrane core of lower microtubule density. Formation of this pattern was inhibited when dynein-dependent transport was perturbed or when membranes were depleted from the extracts. Asters in membrane-depleted extracts were able to move away from the most proximal wall but failed to center in cylindrical enclosures with diameters greater than or equal to 150 µm. Taken as whole, our data suggest that the dynein-dependent transport of membranes buttresses microtubules near the aster center and that this plays an important role in modulating aster architecture and position. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text].

Multiple asters organize the yolk microtubule network during dclk2-GFP zebrafish epiboly

It is known that the organization of microtubule (MT) networks in cells is orchestrated by subcellular structures named MT organizing centers (MTOCs). In this work, we use Light Sheet Fluorescence and Confocal Microscopy to investigate how the MT network surrounding the spherical yolk is arranged in the dclk2-GFP zebrafish transgenic line. We found that during epiboly the MT network is organized by multiple aster-like MTOCS. These structures form rings around the yolk sphere. Importantly, in wt embryos, aster-like MTOCs are only found upon pharmacological or genetic induction. Using our microscopy approach, we underscore the variability in the number of such asters in the transgenic line and report on the variety of global configurations of the yolk MT network. The asters’ morphology, dynamics, and their distribution in the yolk sphere are also analyzed. We propose that these features are tightly linked to epiboly timing and geometry. Key molecules are identified which support this asters role as MTOCs, where MT nucleation and growth take place. We conclude that the yolk MT network of dclk2-GFP transgenic embryos can be used as a model to organize microtubules in a spherical geometry by means of multiple MTOCs.

Spatial and Temporal Scaling of Microtubules and Mitotic Spindles

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

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.

Self-Organization of Cellular Units

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

The Cytoskeleton and Its Roles in Self-Organization Phenomena: Insights from Xenopus Egg Extracts

Self-organization of and by the cytoskeleton is central to the biology of the cell. Since their introduction in the early 1980s, cytoplasmic extracts derived from the eggs of the African clawed-frog, Xenopus laevis, have flourished as a major experimental system to study the various facets of cytoskeleton-dependent self-organization. Over the years, the many investigations that have used these extracts uniquely benefited from their simplified cell cycle, large experimental volumes, biochemical tractability and cell-free nature. Here, we review the contributions of egg extracts to our understanding of the cytoplasmic aspects of self-organization by the microtubule and the actomyosin cytoskeletons as well as the importance of cytoskeletal filaments in organizing nuclear structure and function.

Spatial variation of microtubule depolymerization in large asters

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

Co-movement of astral microtubules, organelles and F-actin by dynein and actomyosin forces in frog egg cytoplasm

How bulk cytoplasm generates forces to separate post-anaphase microtubule (MT) asters in Xenopus laevis and other large eggs remains unclear. Previous models proposed that dynein-based, inward organelle transport generates length-dependent pulling forces that move centrosomes and MTs outwards, while other components of cytoplasm are static. We imaged aster movement by dynein and actomyosin forces in Xenopus egg extracts and observed outward co-movement of MTs, endoplasmic reticulum (ER), mitochondria, acidic organelles, F-actin, keratin, and soluble fluorescein. Organelles exhibited a burst of dynein-dependent inward movement at the growing aster periphery, then mostly halted inside the aster, while dynein-coated beads moved to the aster center at a constant rate, suggesting organelle movement is limited by brake proteins or other sources of drag. These observations call for new models in which all components of the cytoplasm comprise a mechanically integrated aster gel that moves collectively in response to dynein and actomyosin forces.

The nucleus serves as the pacemaker for the cell cycle

Mitosis is a dramatic process that affects all parts of the cell. It is driven by an oscillator whose various components are localized in the nucleus, centrosome, and cytoplasm. In principle, the cellular location with the fastest intrinsic rhythm should act as a pacemaker for the process. Here we traced the waves of tubulin polymerization and depolymerization that occur at mitotic entry and exit in Xenopus egg extracts back to their origins. We found that mitosis was commonly initiated at sperm-derived nuclei and their accompanying centrosomes. The cell cycle was ~20% faster at these initiation points than in the slowest regions of the extract. Nuclei produced from phage DNA, which did not possess centrosomes, also acted as trigger wave sources, but purified centrosomes in the absence of nuclei did not. We conclude that the nucleus accelerates mitotic entry and propose that it acts as a pacemaker for cell cycle.

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

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

Cell Biology: Social Distancing of Microtubule Ends Increases Their Assembly Rates

Microtubules assembled from artificial centrosomes in microfluidic chambers of defined size are amenable to high resolution live imaging of their dynamics and space-filling properties. By using this experimental regime in conjunction with cytoplasmic extract, a new study finds that microtubule end density negatively influences their assembly rates.

Microtubule Growth Rates Are Sensitive to Global and Local Changes in Microtubule Plus-End Density

The microtubule cytoskeleton plays critically important roles in numerous cellular functions in eukaryotes, and it does so across a functionally diverse and morphologically disparate range of cell types [1]. In these roles, microtubule assemblies must adopt distinct morphologies and physical dimensions to perform specific functions [2-5]. As such, these macromolecular assemblies-as well as the dynamics of the individual microtubule polymers from which they are made-must scale and change in accordance with cell size, geometry, and function. Microtubules in cells typically assemble to a steady state in mass, leaving enough of their tubulin subunits soluble to allow rapid growth and turnover. This suggests some negative feedback that limits the extent of assembly, for example, decrease in growth rate, or increase in catastrophe rate, as the soluble subunit pool decreases. Although these ideas have informed the field for decades, they have not been observed experimentally. Here, we describe the application of an experimental approach that combines cell-free extracts with photo-patterned hydrogel micro-enclosures as a means to investigate microtubule dynamics in cytoplasmic volumes of defined size and shape. Our measurements reveal a negative correlation between microtubule plus-end density and microtubule growth rates and suggest that these rates are sensitive to the presence of nearby growing ends.

Microtubule-Based Mechanisms of Pronuclear Positioning

The zygote is defined as a diploid cell resulting from the fusion of two haploid gametes. Union of haploid male and female pronuclei in many animals occurs through rearrangements of the microtubule cytoskeleton into a radial array of microtubules known as the sperm aster. The sperm aster nucleates from paternally-derived centrioles attached to the male pronucleus after fertilization. Nematode, echinoderm, and amphibian eggs have proven as invaluable models to investigate the biophysical principles for how the sperm aster unites male and female pronuclei with precise spatial and temporal regulation. In this review, we compare these model organisms, discussing the dynamics of sperm aster formation and the different force generating mechanism for sperm aster and pronuclear migration. Finally, we provide new mechanistic insights for how sperm aster growth may influence sperm aster positioning.

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

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

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

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

Direct observation of branching MT nucleation in living animal cells

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

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

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

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

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

Spatiotemporal organization of branched microtubule networks

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

The Physics of the Metaphase Spindle

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

Insight into microtubule nucleation from tubulin-capping proteins

Nucleation is one of the least understood steps of microtubule dynamics. It is a kinetically unfavorable process that is templated in the cell by the γ-tubulin ring complex or by preexisting microtubules; it also occurs in vitro from pure tubulin. Here we study the nucleation inhibition potency of natural or artificial proteins in connection with their binding mode to the longitudinal surface of α- or β-tubulin. The structure of tubulin-bound CopN, a Chlamydia protein that delays nucleation, suggests that this protein may interfere with two protofilaments at the (+) end of a nucleus. Designed ankyrin repeat proteins that share a binding mode similar to that of CopN also impede nucleation, whereas those that target only one protofilament do not. In addition, an αRep protein predicted to target two protofilaments at the (-) end does not delay nucleation, pointing to different behaviors at both ends of the nucleus. Our results link the interference with protofilaments at the (+) end and the inhibition of nucleation.

Microtubule plus-ends act as physical signaling hubs to activate RhoA during cytokinesis

Microtubules (MTs) are essential for cleavage furrow positioning during cytokinesis, but the mechanisms by which MT-derived signals spatially define regions of cortical contractility are unresolved. In this study cytokinesis regulators visualized in Drosophila melanogaster (Dm) cells were found to localize to and track MT plus-ends during cytokinesis. The RhoA GEF Pebble (Dm ECT2) did not evidently tip-track, but rather localized rapidly to cortical sites contacted by MT plus-tips, resulting in RhoA activation and enrichment of myosin-regulatory light chain. The MT plus-end localization of centralspindlin was compromised following EB1 depletion, which resulted in a higher incidence of cytokinesis failure. Centralspindlin plus-tip localization depended on the C-terminus and a putative EB1-interaction motif (hxxPTxh) in RacGAP50C. We propose that MT plus-end-associated centralspindlin recruits a cortical pool of Dm ECT2 upon physical contact to activate RhoA and to trigger localized contractility.

Aurora-PLK1 cascades as key signaling modules in the regulation of mitosis

Mitosis is controlled by reversible protein phosphorylation involving specific kinases and phosphatases. A handful of major mitotic protein kinases, such as the cyclin B-CDK1 complex, the Aurora kinases, and Polo-like kinase 1 (PLK1), cooperatively regulate distinct mitotic processes. Research has identified proteins and mechanisms that integrate these kinases into signaling cascades that guide essential mitotic events. These findings have important implications for our understanding of the mechanisms of mitotic regulation and may advance the development of novel antimitotic drugs. We review collected evidence that in vertebrates, the Aurora kinases serve as catalytic subunits of distinct complexes formed with the four scaffold proteins Bora, CEP192, INCENP, and TPX2, which we deem "core" Aurora cofactors. These complexes and the Aurora-PLK1 cascades organized by Bora, CEP192, and INCENP control crucial aspects of mitosis and all pathways of spindle assembly. We compare the mechanisms of Aurora activation in relation to the different spindle assembly pathways and draw a functional analogy between the CEP192 complex and the chromosomal passenger complex that may reflect the coevolution of centrosomes, kinetochores, and the actomyosin cleavage apparatus. We also analyze the roles and mechanisms of Aurora-PLK1 signaling in the cell and centrosome cycles and in the DNA damage response.

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

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

Assembly of Spindles and Asters in Xenopus Egg Extracts

Here, we provide methods for assembly of mitotic spindles and interphase asters in Xenopus laevis egg extract, and compare them to spindles and asters in the egg and zygote. Classic "cycled" spindles are made by adding sperm nuclei to metaphase-arrested cytostatic factor (CSF) extract and inducing entry into interphase extract to promote nucleus formation and DNA replication. Interphase nuclei are then converted to cycled spindles arrested in metaphase by addition of CSF extract. Kinetochores assemble in this reaction and these spindles can segregate chromosomes. CSF spindles are made by addition of sperm nuclei to CSF extract. They are less physiological and lack functional kinetochores but suffice for some applications. Large interphase asters are prepared by addition of artificial centrosomes or sperm nuclei to actin-intact egg extract. These asters grow rapidly to hundreds of microns in radius by branching microtubule nucleation at the periphery, so the aster as a whole is a network of short, dynamic microtubules. They resemble the sperm aster after fertilization, and the asters that grow out of the poles of the mitotic spindle at anaphase. When interphase asters grow into each other they interact and assemble aster interaction zones at their shared boundary. These zones consist of a line (in extract) or disc (in zygotes) of antiparallel microtubule bundles coated with cytokinesis midzone proteins. Interaction zones block interpenetration of microtubules from the two asters, and signal to the cortex to induce cleavage furrows. Their reconstitution in extract allows dissection of the biophysics of spatially regulated cytokinesis signaling.

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

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

Fluctuations uncover a distinct class of traveling waves

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is -1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought.

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

Regulation of size and growth is a fundamental problem in biology. A prominent example is the formation of the mitotic spindle, where protein concentration gradients around chromosomes are thought to regulate spindle growth by controlling microtubule nucleation. Previous evidence suggests that microtubules nucleate throughout the spindle structure. However, the mechanisms underlying microtubule nucleation and its spatial regulation are still unclear. Here, we developed an assay based on laser ablation to directly probe microtubule nucleation events in Xenopus laevis egg extracts. Combining this method with theory and quantitative microscopy, we show that the size of a spindle is controlled by autocatalytic growth of microtubules, driven by microtubule-stimulated microtubule nucleation. The autocatalytic activity of this nucleation system is spatially regulated by the limiting amounts of active microtubule nucleators, which decrease with distance from the chromosomes. This mechanism provides an upper limit to spindle size even when resources are not limiting.

Spindle-to-Cortex Communication in Cleaving Frog Eggs

During cytokinesis, the mitotic spindle communicates with the cell cortex to position a cleavage furrow that will cut through the cell in the plane defined by the metaphase plate. We investigated the molecular basis of this communication in Xenopus laevis eggs, where the signal has to travel ∼400 µm in ∼30 min to reach the cortex from the first anaphase spindle. At anaphase onset, huge microtubule asters grow out from the poles of the spindle and meet at the plane previously defined by the metaphase plate. This disc-shaped boundary plane recruits the chromosome passenger complex (CPC) and centralspindlin to antiparallel microtubule bundles. It grows out to the cell cortex as the asters expand, where it induces the furrow. CPC and centralspindlin were not recruited to boundaries between asters from different spindles, suggesting a role of chromatin in triggering the CPC-positive state. Recruitment of CPC to aster boundaries was reconstituted in an extract system, and we observed that recruitment was stimulated by proximity to chromatin. Finally, we discuss models for molecular processes involved in initiation and growth of the CPC-positive disc that communicates the position of the metaphase plate to the cortex over hundreds of micrometers in frog eggs.

Prc1E and Kif4A control microtubule organization within and between large Xenopus egg asters

The cleavage furrow in Xenopus zygotes is positioned by two large microtubule asters that grow out from the poles of the first mitotic spindle. Where these asters meet at the midplane, they assemble a disk-shaped interaction zone consisting of anti-parallel microtubule bundles coated with chromosome passenger complex (CPC) and centralspindlin that instructs the cleavage furrow. Here we investigate the mechanism that keeps the two asters separate and forms a distinct boundary between them, focusing on the conserved cytokinesis midzone proteins Prc1 and Kif4A. Prc1E, the egg orthologue of Prc1, and Kif4A were recruited to anti-parallel bundles at interaction zones between asters in Xenopus egg extracts. Prc1E was required for Kif4A recruitment but not vice versa. Microtubule plus-end growth slowed and terminated preferentially within interaction zones, resulting in a block to interpenetration that depended on both Prc1E and Kif4A. Unexpectedly, Prc1E and Kif4A were also required for radial order of large asters growing in isolation, apparently to compensate for the direction-randomizing influence of nucleation away from centrosomes. We propose that Prc1E and Kif4, together with catastrophe factors, promote "anti-parallel pruning" that enforces radial organization within asters and generates boundaries to microtubule growth between asters.

Tau-based fluorescent protein fusions to visualize microtubules

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

Cytoskeleton Dynamics: Mind the Gap!

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