Branched microtubule nucleation and dynein transport organize RanGTP asters in Xenopus laevis egg extract.

Chromosome segregation relies on the correct assembly of a bipolar spindle. Spindle pole self-organization requires dynein-dependent microtubule (MT) transport along other MTs. However, during M-phase RanGTP triggers MT nucleation and branching generating polarized arrays with nonastral organization in which MT minus ends are linked to the sides of other MTs. This raises the question of how branched-MT nucleation and dynein-mediated transport cooperate to organize the spindle poles. Here, we used RanGTP-dependent MT aster formation in Xenopus laevis (X. laevis) egg extract to study the interplay between these two seemingly conflicting organizing principles. Using temporally controlled perturbations of MT nucleation and dynein activity, we found that branched MTs are not static but instead dynamically redistribute over time as poles self-organize. Our experimental data together with computer simulations suggest a model where dynein together with dynactin and NuMA directly pulls and move branched MT minus ends toward other MT minus ends.

A Typical Workflow to Simulate Cytoskeletal Systems.

Many cytoskeletal systems are now sufficiently well known to permit their precise quantitative modeling. Microtubule and actin filaments are well characterized, and the associated proteins are often known, as well as their abundance and the interactions between these elements. Thus, computer simulations can be used to investigate the collective behavior of the system precisely, in a way that is complementary to experiments. Cytosim is an Open Source cytoskeleton simulation suite designed to handle large systems of flexible filaments with associated proteins such as molecular motors. It also offers the possibility to simulate passive crosslinkers, diffusible crosslinkers, nucleators, cutters, and discrete versions of the motors that only step on unoccupied lattice sites on a filament. Other objects complement the filaments by offering spherical or more complicated geometry that can be used to represent chromosomes, the nucleus, or vesicles in the cell. Cytosim offers simple command-line tools for running a simulation and displaying its results, which are versatile and do not require programming skills. In this workflow, step-by-step instructions are given to i) install the necessary environment on a new computer, ii) configure Cytosim to simulate the contraction of a 2D actomyosin network, and iii) produce a visual representation of the system. Next, the system is probed by systematically varying a key parameter: the number of crosslinkers. Finally, the visual representation of the system is complemented by the numerical quantification of contractility to view, in a graph, how contractility depends on the composition of the system. Overall, these different steps constitute a typical workflow that can be applied with few modifications to tackle many other problems in the cytoskeletal field.

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.

Effects of microtubule length and crowding on active microtubule network organization.

Active filament networks can organize into various dynamic architectures driven by cross-linking motors. Densities and kinetic properties of motors and microtubules have been shown previously to determine active microtubule network self-organization, but the effects of other control parameters are less understood. Using computer simulations, we study here how microtubule lengths and crowding effects determine active network architecture and dynamics. We find that attractive interactions mimicking crowding effects or long microtubules both promote the formation of extensile nematic networks instead of asters. When microtubules are very long and the network is highly connected, a new isotropically motile network state resembling a "gliding mesh" is predicted. Using in vitro reconstitutions, we confirm the existence of this gliding mesh experimentally. These results provide a better understanding of how active microtubule network organization can be controlled, with implications for cell biology and active materials in general.

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.

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.

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

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

Rab27a co-ordinates actin-dependent transport by controlling organelle-associated motors and track assembly proteins.

Cell biologists generally consider that microtubules and actin play complementary roles in long- and short-distance transport in animal cells. On the contrary, using melanosomes of melanocytes as a model, we recently discovered that the motor protein myosin-Va works with dynamic actin tracks to drive long-range organelle dispersion in opposition to microtubules. This suggests that in animals, as in yeast and plants, myosin/actin can drive long-range transport. Here, we show that the SPIRE-type actin nucleators (predominantly SPIRE1) are Rab27a effectors that co-operate with formin-1 to generate actin tracks required for myosin-Va-dependent transport in melanocytes. Thus, in addition to melanophilin/myosin-Va, Rab27a can recruit SPIREs to melanosomes, thereby integrating motor and track assembly activity at the organelle membrane. Based on this, we suggest a model in which organelles and force generators (motors and track assemblers) are linked, forming an organelle-based, cell-wide network that allows their collective activity to rapidly disperse the population of organelles long-distance throughout the cytoplasm.

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.

The 2020 motile active matter roadmap.

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Insights from graph theory on the morphologies of actomyosin networks with multilinkers.

Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be used to adequately describe this complex process. In this paper we investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher-order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments, as well as the global features of actomyosin networks. We first map the networks into local graph representations and then, using principles from network-theory order parameters, combine properties from these representations to gain insight into the heterogeneous morphologies of actomyosin networks at a global level. We find that ABPs with a valency greater than 2 promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosinlike motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosin detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape.

Theory of antiparallel microtubule overlap stabilization by motors and diffusible crosslinkers.

Antiparallel microtubule bundles are essential structural elements of many cytoskeletal structures, for instance, the mitotic spindle. Sliding of microtubules relative to each other can lead to an overall elongation of the bundle. However, such sliding must be accompanied by microtubule growth, to maintain the overlap, which is a landmark of anaphase. Diffusive crosslinkers of the Ase1/PRC1/MAP65 family are able to form stable overlaps in combination with kinesin-14 motors. This process is thought to arise through a balance of forces between motors and crosslinkers, the latter effectively producing an entropic pressure. We provide a continuous theory to explain the formation of stable overlaps, in which steric effects caused by the finite number of binding sites available on the microtubule lattice play a leading role. We confirmed the validity of this approach using discrete stochastic simulations performed with the Open Source simulation engine Cytosim. From the densities of motors and crosslinkers, their diffusion rates, and the velocities of motors, the theory predicts the sliding speed of microtubules and explains the force production and breaking effect of crosslinkers and motors containing diffusible microtubule-binding domains. Finally, we discuss a mechanism by which sliding and microtubule growth can be coordinated without the need for fine-tuning the parameters of the system, in line with the known robustness of mitosis.

Self-Organization of Minimal Anaphase Spindle Midzone Bundles.

In anaphase spindles, antiparallel microtubules associate to form tight midzone bundles, as required for functional spindle architecture and correct chromosome segregation. Several proteins selectively bind to these overlaps to control cytokinesis. How midzone bundles assemble is poorly understood. Here, using an in vitro reconstitution approach, we demonstrate that minimal midzone bundles can reliably self-organize in solution from dynamic microtubules, the microtubule crosslinker PRC1, and the motor protein KIF4A. The length of the central antiparallel overlaps in these microtubule bundles is similar to that observed in cells and is controlled by the PRC1/KIF4A ratio. Experiments and computer simulations demonstrate that minimal midzone bundle formation results from promoting antiparallel microtubule crosslinking, stopping microtubule plus-end dynamicity, and motor-driven midzone compaction and alignment. The robustness of this process suggests that a similar self-organization mechanism may contribute to the reorganization of the spindle architecture during the metaphase to anaphase transition in cells.

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 computational model of the early stages of acentriolar meiotic spindle assembly.

The mitotic spindle is an ensemble of microtubules responsible for the repartition of the chromosomal content between the two daughter cells during division. In metazoans, spindle assembly is a gradual process involving dynamic microtubules and recruitment of numerous associated proteins and motors. During mitosis, centrosomes organize and nucleate the majority of spindle microtubules. In contrast, oocytes lack canonical centrosomes but are still able to form bipolar spindles, starting from an initial ball that self-organizes in several hours. Interfering with early steps of meiotic spindle assembly can lead to erroneous chromosome segregation. Although not fully elucidated, this process is known to rely on antagonistic activities of plus end- and minus end-directed motors. We developed a model of early meiotic spindle assembly in mouse oocytes, including key factors such as microtubule dynamics and chromosome movement. We explored how the balance between plus end- and minus end-directed motors, as well as the influence of microtubule nucleation, impacts spindle morphology. In a refined model, we added spatial regulation of microtubule stability and minus-end clustering. We could reproduce the features of early stages of spindle assembly from 12 different experimental perturbations and predict eight additional perturbations. With its ability to characterize and predict chromosome individualization, this model can help deepen our understanding of spindle assembly.

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.

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.

F-Actin nucleated on chromosomes coordinates their capture by microtubules in oocyte meiosis.

Capture of each and every chromosome by spindle microtubules is essential to prevent chromosome loss and aneuploidy. In somatic cells, astral microtubules search and capture chromosomes forming lateral attachments to kinetochores. However, this mechanism alone is insufficient in large oocytes. We have previously shown that a contractile F-actin network is additionally required to collect chromosomes scattered in the 70-µm starfish oocyte nucleus. How this F-actin-driven mechanism is coordinated with microtubule capture remained unknown. Here, we show that after nuclear envelope breakdown Arp2/3-nucleated F-actin "patches" form around chromosomes in a Ran-GTP-dependent manner, and we propose that these structures sterically block kinetochore-microtubule attachments. Once F-actin-driven chromosome transport is complete, coordinated disassembly of F-actin patches allows synchronous capture by microtubules. Our observations indicate that this coordination is necessary because early capture of chromosomes by microtubules would interfere with F-actin-driven transport leading to chromosome loss and formation of aneuploid eggs.

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.