A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo

Live-cell imaging under centrifugation characterized the cellular force for nuclear centration in the Caenorhabditis elegans embryo

Organelles in cells are appropriately positioned, despite crowding in the cytoplasm. However, our understanding of the force required to move large organelles, such as the nucleus, inside the cytoplasm is limited, in part owing to a lack of accurate methods for measurement. We devised a novel method to apply forces to the nucleus of living, wild-type Caenorhabditis elegans embryos to measure the force generated inside the cell. We utilized a centrifuge polarizing microscope (CPM) to apply centrifugal force and orientation-independent differential interference contrast (OI-DIC) microscopy to characterize the mass density of the nucleus and cytoplasm. The cellular forces moving the nucleus toward the cell center increased linearly at ~14 pN/μm depending on the distance from the center. The frictional coefficient was ~1,100 pN s/μm. The measured values were smaller than previously reported estimates for sea urchin embryos. The forces were consistent with the centrosome-organelle mutual pulling model for nuclear centration. Frictional coefficient was reduced when microtubules were shorter or detached from nuclei in mutant embryos, demonstrating the contribution of astral microtubules. Finally, the frictional coefficient was higher than a theoretical estimate, indicating the contribution of uncharacterized properties of the cytoplasm.

Nuclear movement in multinucleated cells

Nuclear movement is crucial for the development of many cell types and organisms. Nuclear movement is highly conserved, indicating its necessity for cellular function and development. In addition to mononucleated cells, there are several examples of cells in which multiple nuclei exist within a shared cytoplasm. These multinucleated cells and syncytia have important functions for development and homeostasis. Here, we review a subset of the developmental contexts in which the regulation of the movement and positioning of multiple nuclei are well understood, including pronuclear migration, the Drosophila syncytial blastoderm, the Caenorhabditis elegans hypodermis, skeletal muscle and filamentous fungi. We apply the principles learned from these models to other systems.

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.

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.

Quantifying Intracellular Particle Flows by DIC Object Tracking

Label-free imaging techniques such as differential interference contrast (DIC) allow the observation of cells and large subcellular structures in their native, unperturbed states with minimal exposure to light. The development of robust computational image-analysis routines is vital to quantitative label-free imaging. The reliability of quantitative analysis of time-series microscopy data based on single-particle tracking relies on accurately detecting objects as distinct from the background, i.e., segmentation. Typical approaches to segmenting DIC images either involve converting images to those resembling phase contrast, mimicking the optics of DIC object formation, or using the morphological properties of objects. Here, we describe MATLAB based, single-particle tracking tool with a GUI for mobility analysis of objects from in vitro and in vivo DIC time-series microscopy. The tool integrates contrast enhancement with multiple modified Gaussian filters, automated threshold detection for segmentation and minimal distance-based two-dimensional single-particle tracking. We compare the relative performance of multiple filters and demonstrate the utility of the tool for DIC object tracking (DICOT). We quantify subcellular dynamics of a time series of Caenorhabditis elegans embryos in the one-celled stage by detecting birefringent yolk granules in the cytoplasm with high precision. The resulting two-dimensional map of oscillatory dynamics of granules quantifies the cytoplasmic flows driven by anaphasic spindle oscillations. The frequency of oscillations across the anterior-posterior (A-P) and transverse axes of the embryo correspond well with the reported frequency of spindle oscillations. We validate the quantitative accuracy of our method by tracking the in vitro diffusive mobility of micron-sized beads in glycerol solutions. Estimates of the diffusion coefficients of the granules are used to measure the viscosity of a dilution series of glycerol. Thus, our computational method is likely to be useful for both intracellular mobility and in vitro microrheology.

Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation require a threshold density of both cortical dyneins and coupling kinesins, while the onset is diffusion-limited with relation to the cortical dynein mobility. The coordinated rotational motion emerges due to the resolution of a 'tug-of-war' of multiple cortical dynein motors bound to MTs of the same aster by 'noise' in the form of MT dynamic instability. This transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests that biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in the presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to the particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

Mesoscopic dynamic model of epithelial cell division with cell-cell junction effects

Cell division is central for embryonic development, tissue morphogenesis, and tumor growth. Experiments have evidenced that mitotic cell division is manipulated by the intercellular cues such as cell-cell junctions. However, it still remains unclear how these cortical-associated cues mechanically affect the mitotic spindle machinery, which determines the position and orientation of the cell division. In this paper, a mesoscopic dynamic cell division model is established to explore the integrated regulations of cortical polarity, microtubule pulling forces, cell deformability, and internal osmotic pressure. We show that the distributed pulling forces of astral microtubules play a key role in encoding the instructive cortical cues to orient and position the spindle of a dividing cell. The present model can not only predict the spindle orientation and position, but also capture the morphological evolution of cell rounding. The theoretical results agree well with relevant experiments both qualitatively and quantitatively. This work sheds light on the mechanical linkage between cell cortex and mitotic spindle, and holds potential in regulating cell division and sculpting tissue morphology.

Centering and Shifting of Centrosomes in Cells

Centrosomes have a nonrandom localization in the cells: either they occupy the centroid of the zone free of the actomyosin cortex or they are shifted to the edge of the cell, where their presence is justified from a functional point of view, for example, to organize additional microtubules or primary cilia. This review discusses centrosome placement options in cultured and in situ cells. It has been proven that the central arrangement of centrosomes is due mainly to the pulling microtubules forces developed by dynein located on the cell cortex and intracellular vesicles. The pushing forces from dynamic microtubules and actomyosin also contribute, although the molecular mechanisms of their action have not yet been elucidated. Centrosomal displacement is caused by external cues, depending on signaling, and is drawn through the redistribution of dynein, the asymmetrization of microtubules through the capture of their plus ends, and the redistribution of actomyosin, which, in turn, is associated with basal-apical cell polarization.

Centering and symmetry breaking in confined contracting actomyosin networks

Centering and decentering of cellular components is essential for internal organization of cells and their ability to perform basic cellular functions such as division and motility. How cells achieve proper localization of their organelles is still not well-understood, especially in large cells such as oocytes. Here, we study actin-based positioning mechanisms in artificial cells with persistently contracting actomyosin networks, generated by encapsulating cytoplasmic Xenopus egg extracts into cell-sized ‘water-in-oil’ droplets. We observe size-dependent localization of the contraction center, with a symmetric configuration in larger cells and a polar one in smaller cells. Centering is achieved via a hydrodynamic mechanism based on Darcy friction between the contracting network and the surrounding cytoplasm. During symmetry breaking, transient attachments to the cell boundary drive the contraction center to a polar location. The centering mechanism is cell-cycle dependent and weakens considerably during interphase. Our findings demonstrate a robust, yet tunable, mechanism for subcellular localization.

In order to survive, cells need to react to their environment and change their shape or the localization of their internal components. For example, the nucleus – the compartment that contains the genetic information – is often localized at the center of the cell, but it can also be positioned at the side, for instance when cells move or divide asymmetrically.

Cells use multiple positioning mechanisms to move their internal components, including a process that relies on networks of filaments made of a protein known as actin. These networks are constantly remodeled as actin proteins are added and removed from the network. Embedded molecular motors can cause the network of actin filaments to contract and push or pull on the compartments. Yet, the exact way these networks localize components in the cell remains unclear, especially in eggs and other large cells.

To investigate this question, Ierushalmi et al. studied the actin networks in artificial cells that they created by enclosing the contents of frog eggs in small droplets surrounded by oil. This showed that the networks contracted either to the center of the cell or to its side. Friction between the contracting actin network and the fluid in the cell generated a force that tends to push the contraction center towards the middle of the cell. In larger cells, this led to the centering of the actin network. In smaller cells however, the network transiently attached to the boundary of the cell, leading the contraction center to be pulled to one side.

By developing simpler artificial cells that mimic the positioning processes seen in real-life cells, Ierushalmi et al. discovered new mechanisms for how cells may center or de-center their components. This knowledge may be useful to understand diseases that can emerge when the nucleus or other compartments fail to move to the right location, and which are associated with certain organs developing incorrectly.

Cilia and centrosomes: Ultrastructural and mechanical perspectives

Cilia and centrosomes of eukaryotic cells play important roles in cell movement, fluid transport, extracellular sensing, and chromosome division. The physiological functions of cilia and centrosomes are generated by their dynamics, motions, and forces controlled by the physical, chemical, and biological environments. How an individual cilium achieves its beat pattern and induces fluid flow is governed by its ultrastructure as well as the coordination of associated molecular motors. Thus, a bottom-up understanding of the physiological functions of cilia and centrosomes from the molecular to tissue levels is required. Correlations between the structure and motion can be understood in terms of mechanics. This review first focuses on cilia and centrosomes at the molecular level, introducing their ultrastructure. We then shift to the organelle level and introduce the kinematics and mechanics of cilia and centrosomes. Next, at the tissue level, we introduce nodal ciliary dynamics and nodal flow, which play crucial roles in the organogenetic process of left-right asymmetry. We also introduce respiratory ciliary dynamics and mucous flow, which are critical for protecting the epithelium from drying and exposure to harmful particles and viruses, i.e., respiratory clearance function. Finally, we discuss the future research directions in this field.

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.

Cytoskeleton Force Exertion in Bulk Cytoplasm

The microtubule and actin cytoskeletons generate forces essential to position centrosomes, nuclei, and spindles for division plane specification. While the largest body of work has documented force exertion at, or close to the cell surface, mounting evidence suggests that cytoskeletal polymers can also produce significant forces directly from within the cytoplasm. Molecular motors such as kinesin or dynein may for instance displace cargos and endomembranes in the viscous cytoplasm yielding friction forces that pull or push microtubules. Similarly, the dynamics of bulk actin assembly/disassembly or myosin-dependent contractions produce cytoplasmic forces which influence the spatial organization of cells in a variety of processes. We here review the molecular and physical mechanisms supporting bulk cytoplasmic force generation by the cytoskeleton, their limits and relevance to organelle positioning, with a particular focus on cell division.

Controlling organization and forces in active matter through optically defined boundaries

Living systems are capable of locomotion, reconfiguration and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, 'active' molecules that create and manipulate non-equilibrium structures and force fields of up to millimetre length scales1-3. Experimental active-matter systems of biological or synthetic molecules are capable of spontaneously organizing into structures4,5 and generating global flows6-9. However, these experimental systems lack the spatiotemporal control found in cells, limiting their utility for studying non-equilibrium phenomena and bioinspired engineering. Here we uncover non-equilibrium phenomena and principles of boundary-mediated control by optically modulating structures and fluid flow in an engineered system of active biomolecules. Our system consists of purified microtubules and light-activatable motor proteins that crosslink and organize the microtubules into distinct structures upon illumination. We develop basic operations-defined as sets of light patterns-to create, move and merge the microtubule structures. By combining these operations, we create microtubule networks that span several hundred micrometres in length and contract at speeds up to an order of magnitude higher than the speed of an individual motor protein. We manipulate these contractile networks to generate and sculpt persistent fluid flows. The principles of boundary-mediated control that we uncover may be used to study emergent cellular structures and forces and to develop programmable active-matter devices.

Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales

The combination of fluid-structure interactions with stochasticity, due to thermal fluctuations, remains a challenging problem in computational fluid dynamics. We develop an efficient scheme based on the stochastic immersed boundary method, Stokeslets, and multiple timestepping. We test our method for spherical particles and filaments under purely thermal and deterministic forces and find good agreement with theoretical predictions for Brownian Motion of a particle and equilibrium thermal undulations of a semi-flexible filament. As an initial application, we simulate bio-filaments with the properties of F-actin. We specifically study the average time for two nearby parallel filaments to bundle together. Interestingly, we find a two-fold acceleration in this time between simulations that account for long-range hydrodynamics compared to those that do not, suggesting that our method will reveal significant hydrodynamic effects in biological phenomena.

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.

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.

Different bending models predict different dynamics of sedimenting elastic trumbbells

The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at low-Reynolds-number. We use the bead-spring approximation of a filament and the Rotne-Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or - alternatively - by the 'cosine' (also called the Kratky-Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic long-lasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky-Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky-Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads well-separated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own.

Uncovering the balance of forces driving microtubule aster migration in C. elegans zygotes

Microtubule asters must be positioned precisely within cells. How forces generated by molecular motors such as dynein are integrated in space and time to enable such positioning remains unclear. In particular, whereas aster movements depend on the drag caused by cytoplasm viscosity, in vivo drag measurements are lacking, precluding a thorough understanding of the mechanisms governing aster positioning. Here, we investigate this fundamental question during the migration of asters and pronuclei in C. elegans zygotes, a process essential for the mixing of parental genomes. Detailed quantification of these movements using the female pronucleus as an in vivo probe establish that the drag coefficient of the male-asters complex is approximately five times that of the female pronucleus. Further analysis of embryos lacking cortical dynein, the connection between asters and male pronucleus, or the male pronucleus altogether, uncovers the balance of dynein-driven forces that accurately position microtubule asters in C. elegans zygotes.

Microtubule asters are positioned precisely within cells by forces generated by molecular motors, but it is unclear how these are integrated in space and time. Here the authors perform in vivo drag measurements and genetic manipulations to determine the balance of forces that position microtubule asters in C. elegans zygotes.

Cytoplasmic flows as signatures for the mechanics of mitotic positioning

The proper positioning of mitotic spindle in the single-cell Caenorhabditis elegans embryo is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated astral microtubules (MTs). Pronuclear migration produces global cytoplasmic flows that couple the mechanics of all MTs, the PNC, and the cell periphery with each other through their hydrodynamic interactions (HIs). We present the first computational study that explicitly accounts for detailed HIs between the cytoskeletal components and demonstrate the key consequences of HIs for the mechanics of pronuclear migration. First, we show that, because of HIs between the MTs, the cytoplasm-filled astral MTs behave like a porous medium, with its permeability decreasing with increasing the number of MTs. We then directly study the dynamics of PNC migration under various force-transduction models, including the pushing or pulling of MTs at the cortex and the pulling of MTs by cytoplasmically bound force generators. Although achieving proper position and orientation on reasonable time scales does not uniquely choose a model, we find that each model produces a different signature in its induced cytoplasmic flow. We suggest that cytoplasmic flows can be used to differentiate between mechanisms.

Dynactin binding to tyrosinated microtubules promotes centrosome centration in C. elegans by enhancing dynein-mediated organelle transport

The microtubule-based motor dynein generates pulling forces for centrosome centration and mitotic spindle positioning in animal cells. How the essential dynein activator dynactin regulates these functions of the motor is incompletely understood. Here, we dissect the role of dynactin's microtubule binding activity, located in the p150 CAP-Gly domain and an adjacent basic patch, in the C. elegans zygote. Analysis of p150 mutants engineered by genome editing suggests that microtubule tip tracking of dynein-dynactin is dispensable for targeting the motor to the cell cortex and for generating robust cortical pulling forces. Instead, mutations in p150's CAP-Gly domain inhibit cytoplasmic pulling forces responsible for centration of centrosomes and attached pronuclei. The centration defects are mimicked by mutations of α-tubulin's C-terminal tyrosine, and both p150 CAP-Gly and tubulin tyrosine mutants decrease the frequency of early endosome transport from the cell periphery towards centrosomes during centration. Our results suggest that p150 GAP-Gly domain binding to tyrosinated microtubules promotes initiation of dynein-mediated organelle transport in the dividing one-cell embryo, and that this function of p150 is critical for generating cytoplasmic pulling forces for centrosome centration.

C. elegans chromosomes connect to centrosomes by anchoring into the spindle network

The mitotic spindle ensures the faithful segregation of chromosomes. Here we combine the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging to reconstruct all microtubules in 3D and identify their plus- and minus-ends. We classify them as kinetochore (KMTs), spindle (SMTs) or astral microtubules (AMTs) according to their positions, and quantify distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.

A connection between centrosomes and chromosomes is a key feature of mitotic spindles. Here the authors generate 3D reconstructions of whole mitotic spindles in early C. elegans embryos and show that chromosomes are anchored by the entire spindle network and that connections through kinetochore microtubules are few and likely very transient.

Forces positioning the mitotic spindle: Theories, and now experiments

The position of the spindle determines the position of the cleavage plane, and is thus crucial for cell division. Although spindle positioning has been extensively studied, the underlying forces ultimately responsible for moving the spindle remain poorly understood. A recent pioneering study by Garzon-Coral et al. uses magnetic tweezers to perform the first direct measurements of the forces involved in positioning the mitotic spindle. Combining this with molecular perturbations and geometrical effects, they use their data to argue that the forces that keep the spindle in its proper position for cell division arise from astral microtubules growing and pushing against the cell's cortex. Here, we review these ground-breaking experiments, the various biomechanical models for spindle positioning that they seek to differentiate, and discuss new questions raised by these measurements.

Stronger net posterior cortical forces and asymmetric microtubule arrays produce simultaneous centration and rotation of the pronuclear complex in the early Caenorhabditis elegans embryo

Experimental and theoretical approaches are used to demonstrate the importance of asymmetries in microtubule arrays and cortical pulling forces mediated by dynein in positioning the pronuclear complex before nuclear envelope breakdown in the early Caenorhabditis elegans embryo.

Positioning of microtubule-organizing centers (MTOCs) incorporates biochemical and mechanical cues for proper alignment of the mitotic spindle and cell division site. Current experimental and theoretical studies in the early Caenorhabditis elegans embryo assume remarkable changes in the origin and polarity of forces acting on the MTOCs. These changes must occur over a few minutes, between initial centration and rotation of the pronuclear complex and entry into mitosis, and the models do not replicate in vivo timing of centration and rotation. Here we propose a model that incorporates asymmetry in the microtubule arrays generated by each MTOC, which we demonstrate with in vivo measurements, and a similar asymmetric force profile to that required for posterior-directed spindle displacement during mitosis. We find that these asymmetries are capable of and important for recapitulating the simultaneous centration and rotation of the pronuclear complex observed in vivo. The combination of theoretical and experimental evidence provided here offers a unified framework for the spatial organization and forces needed for pronuclear centration, rotation, and spindle displacement in the early C. elegans embryo.

A Mechanism for Cytoplasmic Streaming: Kinesin-Driven Alignment of Microtubules and Fast Fluid Flows

The transport of cytoplasmic components can be profoundly affected by hydrodynamics. Cytoplasmic streaming in Drosophila oocytes offers a striking example. Forces on fluid from kinesin-1 are initially directed by a disordered meshwork of microtubules, generating minor slow cytoplasmic flows. Subsequently, to mix incoming nurse cell cytoplasm with ooplasm, a subcortical layer of microtubules forms parallel arrays that support long-range, fast flows. To analyze the streaming mechanism, we combined observations of microtubule and organelle motions with detailed mathematical modeling. In the fast state, microtubules tethered to the cortex form a thin subcortical layer and undergo correlated sinusoidal bending. Organelles moving in flows along the arrays show velocities that are slow near the cortex and fast on the inward side of the subcortical microtubule layer. Starting with fundamental physical principles suggested by qualitative hypotheses, and with published values for microtubule stiffness, kinesin velocity, and cytoplasmic viscosity, we developed a quantitative coupled hydrodynamic model for streaming. The fully detailed mathematical model and its simulations identify key variables that can shift the system between disordered (slow) and ordered (fast) states. Measurements of array curvature, wave period, and the effects of diminished kinesin velocity on flow rates, as well as prior observations on f-actin perturbation, support the model. This establishes a concrete mechanistic framework for the ooplasmic streaming process. The self-organizing fast phase is a result of viscous drag on kinesin-driven cargoes that mediates equal and opposite forces on cytoplasmic fluid and on microtubules whose minus ends are tethered to the cortex. Fluid moves toward plus ends and microtubules are forced backward toward their minus ends, resulting in buckling. Under certain conditions, the buckling microtubules self-organize into parallel bending arrays, guiding varying directions for fast plus-end directed fluid flows that facilitate mixing in a low Reynolds number regime.

Shape-motion relationships of centering microtubule asters

Although mechanisms that contribute to microtubule (MT) aster positioning have been extensively studied, still little is known on how asters move inside cells to faithfully target a cellular location. Here, we study sperm aster centration in sea urchin eggs, as a stereotypical large-scale aster movement with extreme constraints on centering speed and precision. By tracking three-dimensional aster centration dynamics in eggs with manipulated shapes, we show that aster geometry resulting from MT growth and interaction with cell boundaries dictates aster instantaneous directionality, yielding cell shape-dependent centering trajectories. Aster laser surgery and modeling suggest that dynein-dependent MT cytoplasmic pulling forces that scale to MT length function to convert aster geometry into directionality. In contrast, aster speed remains largely independent of aster size, shape, or absolute dynein activity, which suggests it may be predominantly determined by aster growth rate rather than MT force amplitude. These studies begin to define the geometrical principles that control aster movements.

A physical perspective on cytoplasmic streaming

Organisms show a remarkable range of sizes, yet the dimensions of a single cell rarely exceed 100 µm. While the physical and biological origins of this constraint remain poorly understood, exceptions to this rule give valuable insights. A well-known counterexample is the aquatic plant Chara, whose cells can exceed 10 cm in length and 1 mm in diameter. Two spiralling bands of molecular motors at the cell periphery drive the cellular fluid up and down at speeds up to 100 µm s(-1), motion that has been hypothesized to mitigate the slowness of metabolite transport on these scales and to aid in homeostasis. This is the most organized instance of a broad class of continuous motions known as 'cytoplasmic streaming', found in a wide range of eukaryotic organisms-algae, plants, amoebae, nematodes and flies-often in unusually large cells. In this overview of the physics of this phenomenon, we examine the interplay between streaming, transport and cell size and discuss the possible role of self-organization phenomena in establishing the observed patterns of streaming.

Collective surfing of chemically active particles

We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.

Restarting life: fertilization and the transition from meiosis to mitosis

Fertilization triggers a complex cellular programme that transforms two highly specialized meiotic germ cells, the oocyte and the sperm, into a totipotent mitotic embryo. Linkages between sister chromatids are remodelled to support the switch from reductional meiotic to equational mitotic divisions; the centrosome, which is absent from the egg, is reintroduced; cell division shifts from being extremely asymmetric to symmetric; genomic imprinting is selectively erased and re-established; and protein expression shifts from translational control to transcriptional control. Recent work has started to reveal how this remarkable transition from meiosis to mitosis is achieved.

Cargo transport by cytoplasmic Dynein can center embryonic centrosomes

To complete meiosis II in animal cells, the male DNA material needs to meet the female DNA material contained in the female pronucleus at the egg center, but it is not known how the male pronucleus, deposited by the sperm at the periphery of the cell, finds the cell center in large eggs. Pronucleus centering is an active process that appears to involve microtubules and molecular motors. For small and medium-sized cells, the force required to move the centrosome can arise from either microtubule pushing on the cortex, or cortically-attached dynein pulling on microtubules. However, in large cells, such as the fertilized Xenopus laevis embryo, where microtubules are too long to support pushing forces or they do not reach all boundaries before centrosome centering begins, a different force generating mechanism must exist. Here, we present a centrosome positioning model in which the cytosolic drag experienced by cargoes hauled by cytoplasmic dynein on the sperm aster microtubules can move the centrosome towards the cell's center. We find that small, fast cargoes (diameter ∼100 nm, cargo velocity ∼2 µm/s) are sufficient to move the centrosome in the geometry of the Xenopus laevis embryo within the experimentally observed length and time scales.

Growth, interaction, and positioning of microtubule asters in extremely large vertebrate embryo cells

Ray Rappaport spent many years studying microtubule asters, and how they induce cleavage furrows. Here, we review recent progress on aster structure and dynamics in zygotes and early blastomeres of Xenopus laevis and Zebrafish, where cells are extremely large. Mitotic and interphase asters differ markedly in size, and only interphase asters span the cell. Growth of interphase asters occurs by a mechanism that allows microtubule density at the aster periphery to remain approximately constant as radius increases. We discuss models for aster growth, and favor a branching nucleation process. Neighboring asters that grow into each other interact to block further growth at the shared boundary. We compare the morphology of interaction zones formed between pairs of asters that grow out from the poles of the same mitotic spindle (sister asters) and between pairs not related by mitosis (non-sister asters) that meet following polyspermic fertilization. We argue growing asters recognize each other by interaction between antiparallel microtubules at the mutual boundary, and discuss models for molecular organization of interaction zones. Finally, we discuss models for how asters, and the centrosomes within them, are positioned by dynein-mediated pulling forces so as to generate stereotyped cleavage patterns. Studying these problems in extremely large cells is starting to reveal how general principles of cell organization scale with cell size.