Determinants of Polar versus Nematic Organization in Networks of Dynamic Microtubules and Mitotic Motors.

During cell division, mitotic motors organize microtubules in the bipolar spindle into either polar arrays at the spindle poles or a "nematic" network of aligned microtubules at the spindle center. The reasons for the distinct self-organizing capacities of dynamic microtubules and different motors are not understood. Using in vitro reconstitution experiments and computer simulations, we show that the human mitotic motors kinesin-5 KIF11 and kinesin-14 HSET, despite opposite directionalities, can both organize dynamic microtubules into either polar or nematic networks. We show that in addition to the motor properties the natural asymmetry between microtubule plus- and minus-end growth critically contributes to the organizational potential of the motors. We identify two control parameters that capture system composition and kinetic properties and predict the outcome of microtubule network organization. These results elucidate a fundamental design principle of spindle bipolarity and establish general rules for active filament network organization.

Systematic Nanoscale Analysis of Endocytosis Links Efficient Vesicle Formation to Patterned Actin Nucleation.

Clathrin-mediated endocytosis is an essential cellular function in all eukaryotes that is driven by a self-assembled macromolecular machine of over 50 different proteins in tens to hundreds of copies. How these proteins are organized to produce endocytic vesicles with high precision and efficiency is not understood. Here, we developed high-throughput superresolution microscopy to reconstruct the nanoscale structural organization of 23 endocytic proteins from over 100,000 endocytic sites in yeast. We found that proteins assemble by radially ordered recruitment according to function. WASP family proteins form a circular nanoscale template on the membrane to spatially control actin nucleation during vesicle formation. Mathematical modeling of actin polymerization showed that this WASP nano-template optimizes force generation for membrane invagination and substantially increases the efficiency of endocytosis. Such nanoscale pre-patterning of actin nucleation may represent a general design principle for directional force generation in membrane remodeling processes such as during cell migration and division.

Actin-capping protein regulates actomyosin contractility to maintain germline architecture in C. elegans.

Actin dynamics play an important role in tissue morphogenesis, yet the control of actin filament growth takes place at the molecular level. A challenge in the field is to link the molecular function of actin regulators with their physiological function. Here, we report an in vivo role of the actin-capping protein CAP-1 in the Caenorhabditis elegans germline. We show that CAP-1 is associated with actomyosin structures in the cortex and rachis, and its depletion or overexpression led to severe structural defects in the syncytial germline and oocytes. A 60% reduction in the level of CAP-1 caused a twofold increase in F-actin and non-muscle myosin II activity, and laser incision experiments revealed an increase in rachis contractility. Cytosim simulations pointed to increased myosin as the main driver of increased contractility following loss of actin-capping protein. Double depletion of CAP-1 and myosin or Rho kinase demonstrated that the rachis architecture defects associated with CAP-1 depletion require contractility of the rachis actomyosin corset. Thus, we uncovered a physiological role for actin-capping protein in regulating actomyosin contractility to maintain reproductive tissue architecture.

Katanin contributes to interspecies spindle length scaling in Xenopus.

Bipolar spindles must separate chromosomes by the appropriate distance during cell division, but mechanisms determining spindle length are poorly understood. Based on a 2D model of meiotic spindle assembly, we predicted that higher localized microtubule (MT) depolymerization rates could generate the shorter spindles observed in egg extracts of X. tropicalis compared to X. laevis. We found that katanin-dependent MT severing was increased in X. tropicalis, which, unlike X. laevis, lacks an inhibitory phosphorylation site in the katanin p60 catalytic subunit. Katanin inhibition lengthened spindles in both species. In X. tropicalis, k-fiber MT bundles that connect to chromosomes at their kinetochores extended through spindle poles, disrupting them. In both X. tropicalis extracts and the spindle simulation, a balance between k-fiber number and MT depolymerization is required to maintain spindle morphology. Thus, mechanisms have evolved in different species to scale spindle size and coordinate regulation of multiple MT populations in order to generate a robust steady-state structure.

A self-organization framework for symmetry breaking in the mammalian embryo.

The mechanisms underlying the appearance of asymmetry between cells in the early embryo and consequently the specification of distinct cell lineages during mammalian development remain elusive. Recent experimental advances have revealed unexpected dynamics of and new complexity in this process. These findings can be integrated in a new unified framework that regards the early mammalian embryo as a self-organizing system.

Cross-linker design determines microtubule network organization by opposing motors.

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

Chromatin shapes the mitotic spindle.

In animal and plant cells, mitotic chromatin locally generates microtubules that self-organize into a mitotic spindle, and its dimensions and bipolar symmetry are essential for accurate chromosome segregation. By immobilizing microscopic chromatin-coated beads on slide surfaces using a microprinting technique, we have examined the effect of chromatin on the dimensions and symmetry of spindles in Xenopus laevis cytoplasmic extracts. While circular spots with diameters around 14-18 microm trigger bipolar spindle formation, larger spots generate an incorrect number of poles. We also examined lines of chromatin with various dimensions. Their length determined the number of poles that formed, with a 6 x 18 microm rectangular patch generating normal spindle morphology. Around longer lines, multiple poles formed and the structures were disorganized. While lines thinner than 10 mum generated symmetric structures, thicker lines induced the formation of asymmetric structures where all microtubules are on the same side of the line. Our results show that chromatin defines spindle shape and orientation. For a video summary of this article, see the PaperFlick file available with the online Supplemental Data.

Contractile ring composition dictates kinetics of in silico contractility.

Constriction kinetics of the cytokinetic ring are expected to depend on dynamic adjustment of contractile ring composition, but the impact of ring component abundance dynamics on ring constriction is understudied. Computational models generally assume that contractile networks maintain constant total amounts of components, which is not always true. To test how compositional dynamics affect constriction kinetics, we first measured F-actin, non-muscle myosin II, septin, and anillin during Caenorhabditis elegans zygotic mitosis. A custom microfluidic device that positioned the cell with the division plane parallel to a light sheet allowed even illumination of the cytokinetic ring. Measured component abundances were implemented in a three-dimensional agent-based model of a membrane-associated contractile ring. With constant network component amounts, constriction completed with biologically unrealistic kinetics. However, imposing the measured changes in component quantities allowed this model to elicit realistic constriction kinetics. Simulated networks were more sensitive to changes in motor and filament amounts than those of crosslinkers and tethers. Our findings highlight the importance of network composition for actomyosin contraction kinetics.

Asymmetric division of contractile domains couples cell positioning and fate specification.

During pre-implantation development, the mammalian embryo self-organizes into the blastocyst, which consists of an epithelial layer encapsulating the inner-cell mass (ICM) giving rise to all embryonic tissues. In mice, oriented cell division, apicobasal polarity and actomyosin contractility are thought to contribute to the formation of the ICM. However, how these processes work together remains unclear. Here we show that asymmetric segregation of the apical domain generates blastomeres with different contractilities, which triggers their sorting into inner and outer positions. Three-dimensional physical modelling of embryo morphogenesis reveals that cells internalize only when differences in surface contractility exceed a predictable threshold. We validate this prediction using biophysical measurements, and successfully redirect cell sorting within the developing blastocyst using maternal myosin (Myh9)-knockout chimaeric embryos. Finally, we find that loss of contractility causes blastomeres to show ICM-like markers, regardless of their position. In particular, contractility controls Yap subcellular localization, raising the possibility that mechanosensing occurs during blastocyst lineage specification. We conclude that contractility couples the positioning and fate specification of blastomeres. We propose that this ensures the robust self-organization of blastomeres into the blastocyst, which confers remarkable regulative capacities to mammalian embryos.

Spindle pole body-anchored Kar3 drives the nucleus along microtubules from another nucleus in preparation for nuclear fusion during yeast karyogamy.

Nuclear migration during yeast karyogamy, termed nuclear congression, is required to initiate nuclear fusion. Congression involves a specific regulation of the microtubule minus end-directed kinesin-14 motor Kar3 and a rearrangement of the cytoplasmic microtubule attachment sites at the spindle pole bodies (SPBs). However, how these elements interact to produce the forces necessary for nuclear migration is less clear. We used electron tomography, molecular genetics, quantitative imaging, and first principles modeling to investigate how cytoplasmic microtubules are organized during nuclear congression. We found that Kar3, with the help of its light chain, Cik1, is anchored during mating to the SPB component Spc72 that also serves as a nucleator and anchor for microtubules via their minus ends. Moreover, we show that no direct microtubule-microtubule interactions are required for nuclear migration. Instead, SPB-anchored Kar3 exerts the necessary pulling forces laterally on microtubules emanating from the SPB of the mating partner nucleus. Therefore, a twofold symmetrical application of the core principle that drives nuclear migration in higher cells is used in yeast to drive nuclei toward each other before nuclear fusion.

Bond Type and Discretization of Nonmuscle Myosin II Are Critical for Simulated Contractile Dynamics.

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, cross-link, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is nonmuscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and cross-link actin filaments (F-actin). The multivalence of NMMII ensembles and their multiple roles have confounded the resolution of crucial questions, including how the number of NMMII subunits affects dynamics and what affects the relative contribution of ensembles' cross-linking versus motoring activities. Because biophysical measurements of ensembles are sparse, modeling of actomyosin networks has aided in discovering the complex behaviors of NMMII ensembles. Myosin ensembles have been modeled via several strategies with variable discretization or coarse graining and unbinding dynamics, and although general assumptions that simplify motor ensembles result in global contractile behaviors, it remains unclear which strategies most accurately depict cellular activity. Here, we used an agent-based platform, Cytosim, to implement several models of NMMII ensembles. Comparing the effects of bond type, we found that ensembles of catch-slip and catch motors were the best force generators and binders of filaments. Slip motor ensembles were capable of generating force but unbound frequently, resulting in slower contractile rates of contractile networks. Coarse graining of these ensemble types from two sets of 16 motors on opposite ends of a stiff rod to two binders, each representing 16 motors, reduced force generation, contractility, and the total connectivity of filament networks for all ensemble types. A parallel cluster model, previously used to describe ensemble dynamics via statistical mechanics, allowed better contractility with coarse graining, though connectivity was still markedly reduced for this ensemble type with coarse graining. Together, our results reveal substantial tradeoffs associated with the process of coarse graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.

Polarity sorting drives remodeling of actin-myosin networks.

Cytoskeletal networks of actin filaments and myosin motors drive many dynamic cell processes. A key characteristic of these networks is their contractility. Despite intense experimental and theoretical efforts, it is not clear what mechanism favors network contraction over expansion. Recent work points to a dominant role for the nonlinear mechanical response of actin filaments, which can withstand stretching but buckle upon compression. Here, we present an alternative mechanism. We study how interactions between actin and myosin-2 at the single-filament level translate into contraction at the network scale by performing time-lapse imaging on reconstituted quasi-2D networks mimicking the cell cortex. We observe myosin end-dwelling after it runs processively along actin filaments. This leads to transport and clustering of actin filament ends and the formation of transiently stable bipolar structures. Further, we show that myosin-driven polarity sorting produces polar actin asters, which act as contractile nodes that drive contraction in crosslinked networks. Computer simulations comparing the roles of the end-dwelling mechanism and a buckling-dependent mechanism show that the relative contribution of end-dwelling contraction increases as the network mesh-size decreases.

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

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

Effects of spatial dimensionality and steric interactions on microtubule-motor self-organization.

Active networks composed of filaments and motor proteins can self-organize into a variety of architectures. Computer simulations in two or three spatial dimensions and including or omitting steric interactions between filaments can be used to model active networks. Here we examine how these modelling choices affect the state space of network self-organization. We compare the networks generated by different models of a system of dynamic microtubules and microtubule-crosslinking motors. We find that a thin 3D model that includes steric interactions between filaments is the most versatile, capturing a variety of network states observed in recent experiments. In contrast, 2D models either with or without steric interactions which prohibit microtubule crossings can produce some, but not all, observed network states. Our results provide guidelines for the most appropriate choice of model for the study of different network types and elucidate mechanisms of active network organization.

A theory that predicts behaviors of disordered cytoskeletal networks.

Morphogenesis in animal tissues is largely driven by actomyosin networks, through tensions generated by an active contractile process. Although the network components and their properties are known, and networks can be reconstituted in vitro, the requirements for contractility are still poorly understood. Here, we describe a theory that predicts whether an isotropic network will contract, expand, or conserve its dimensions. This analytical theory correctly predicts the behavior of simulated networks, consisting of filaments with varying combinations of connectors, and reveals conditions under which networks of rigid filaments are either contractile or expansile. Our results suggest that pulsatility is an intrinsic behavior of contractile networks if the filaments are not stable but turn over. The theory offers a unifying framework to think about mechanisms of contractions or expansion. It provides the foundation for studying a broad range of processes involving cytoskeletal networks and a basis for designing synthetic networks.

Membrane Mechanics of Endocytosis in Cells with Turgor.

Endocytosis is an essential process by which cells internalize a piece of plasma membrane and material from the outside. In cells with turgor, pressure opposes membrane deformations, and increases the amount of force that has to be generated by the endocytic machinery. To determine this force, and calculate the shape of the membrane, we used physical theory to model an elastic surface under pressure. Accurate fits of experimental profiles are obtained assuming that the coated membrane is highly rigid and preferentially curved at the endocytic site. The forces required from the actin machinery peaks at the onset of deformation, indicating that once invagination has been initiated, endocytosis is unlikely to stall before completion. Coat proteins do not lower the initiation force but may affect the process by the curvature they induce. In the presence of isotropic curvature inducers, pulling the tip of the invagination can trigger the formation of a neck at the base of the invagination. Hence direct neck constriction by actin may not be required, while its pulling role is essential. Finally, the theory shows that anisotropic curvature effectors stabilize membrane invaginations, and the loss of crescent-shaped BAR domain proteins such as Rvs167 could therefore trigger membrane scission.

Geometrical and mechanical properties control actin filament organization.

The different actin structures governing eukaryotic cell shape and movement are not only determined by the properties of the actin filaments and associated proteins, but also by geometrical constraints. We recently demonstrated that limiting nucleation to specific regions was sufficient to obtain actin networks with different organization. To further investigate how spatially constrained actin nucleation determines the emergent actin organization, we performed detailed simulations of the actin filament system using Cytosim. We first calibrated the steric interaction between filaments, by matching, in simulations and experiments, the bundled actin organization observed with a rectangular bar of nucleating factor. We then studied the overall organization of actin filaments generated by more complex pattern geometries used experimentally. We found that the fraction of parallel versus antiparallel bundles is determined by the mechanical properties of actin filament or bundles and the efficiency of nucleation. Thus nucleation geometry, actin filaments local interactions, bundle rigidity, and nucleation efficiency are the key parameters controlling the emergent actin architecture. We finally simulated more complex nucleation patterns and performed the corresponding experiments to confirm the predictive capabilities of the model.

Collective behavior of minus-ended motors in mitotic microtubule asters gliding toward DNA.

Microtubules (MTs) nucleated by centrosomes form star-shaped structures referred to as asters. Aster motility and dynamics is vital for genome stability, cell division, polarization and differentiation. Asters move either toward the cell center or away from it. Here, we focus on the centering mechanism in a membrane independent system of Xenopus cytoplasmic egg extracts. Using live microscopy and single particle tracking, we find that asters move toward chromatinized DNA structures. The velocity and directionality profiles suggest a random-walk with drift directed toward DNA. We have developed a theoretical model that can explain this movement as a result of a gradient of MT length dynamics and MT gliding on immobilized dynein motors. In simulations, the antagonistic action of the motor species on the radial array of MTs leads to a tug-of-war purely due to geometric considerations and aster motility resembles a directed random-walk. Additionally, our model predicts that aster velocities do not change greatly with varying initial distance from DNA. The movement of asymmetric asters becomes increasingly super-diffusive with increasing motor density, but for symmetric asters it becomes less super-diffusive. The transition of symmetric asters from superdiffusive to diffusive mobility is the result of number fluctuations in bound motors in the tug-of-war. Overall, our model is in good agreement with experimental data in Xenopus cytoplasmic extracts and predicts novel features of the collective effects of motor-MT interactions.

Mechanism of phototaxis in marine zooplankton.

The simplest animal eyes are eyespots composed of two cells only: a photoreceptor and a shading pigment cell. They resemble Darwin's 'proto-eyes', considered to be the first eyes to appear in animal evolution. Eyespots cannot form images but enable the animal to sense the direction of light. They are characteristic for the zooplankton larvae of marine invertebrates and are thought to mediate larval swimming towards the light. Phototaxis of invertebrate larvae contributes to the vertical migration of marine plankton, which is thought to represent the biggest biomass transport on Earth. Yet, despite its ecological and evolutionary importance, the mechanism by which eyespots regulate phototaxis is poorly understood. Here we show how simple eyespots in marine zooplankton mediate phototactic swimming, using the marine annelid Platynereis dumerilii as a model. We find that the selective illumination of one eyespot changes the beating of adjacent cilia by direct cholinergic innervation resulting in locally reduced water flow. Computer simulations of larval swimming show that these local effects are sufficient to direct the helical swimming trajectories towards the light. The computer model also shows that axial rotation of the larval body is essential for phototaxis and that helical swimming increases the precision of navigation. These results provide, to our knowledge, the first mechanistic understanding of phototaxis in a marine zooplankton larva and show how simple eyespots regulate it. We propose that the underlying direct coupling of light sensing and ciliary locomotor control was a principal feature of the proto-eye and an important landmark in the evolution of animal eyes.

Augmin promotes meiotic spindle formation and bipolarity in Xenopus egg extracts.

Female meiotic spindles in many organisms form in the absence of centrosomes, the organelle typically associated with microtubule (MT) nucleation. Previous studies have proposed that these meiotic spindles arise from RanGTP-mediated MT nucleation in the vicinity of chromatin; however, whether this process is sufficient for spindle formation is unknown. Here, we investigated whether a recently proposed spindle-based MT nucleation pathway that involves augmin, an 8-subunit protein complex, also contributes to spindle morphogenesis. We used an assay system in which hundreds of meiotic spindles can be observed forming around chromatin-coated beads after introduction of Xenopus egg extracts. Spindles forming in augmin-depleted extracts showed reduced rates of MT formation and were predominantly multipolar, revealing a function of augmin in stabilizing the bipolar shape of the acentrosomal meiotic spindle. Our studies also have uncovered an apparent augmin-independent MT nucleation process from acentrosomal poles, which becomes increasingly active over time and appears to partially rescue the spindle defects that arise from augmin depletion. Our studies reveal that spatially and temporally distinct MT generation pathways from chromatin, spindle MTs, and acentrosomal poles all contribute to robust bipolar spindle formation in meiotic extracts.