Stress generation and filament turnover during actin ring constriction

Kinetic trapping organizes actin filaments within liquid-like protein droplets

Several actin-binding proteins (ABPs) phase separate to form condensates capable of curating the actin network shapes. Here, we use computational modeling to understand the principles of actin network organization within VASP condensate droplets. Our simulations reveal that the different actin shapes, namely shells, rings, and mixture states are highly dependent on the kinetics of VASP-actin interactions, suggesting that they arise from kinetic trapping. Specifically, we show that reducing the residence time of VASP on actin filaments reduces degree of bundling, thereby promoting assembly of shells rather than rings. We validate the model predictions experimentally using a VASP-mutant with decreased bundling capability. Finally, we investigate the ring opening within deformed droplets and found that the sphere-to-ellipsoid transition is favored under a wide range of filament lengths while the ellipsoid-to-rod transition is only permitted when filaments have a specific range of lengths. Our findings highlight key mechanisms of actin organization within phase-separated ABPs.

Stability of asymmetric cell division: A deformable cell model of cytokinesis applied to C. elegans

Cell division during early embryogenesis is linked to key morphogenic events such as embryo symmetry breaking and tissue patterning. It is thought that the physical surrounding of cells together with cell intrinsic cues act as a mechanical "mold," guiding cell division to ensure these events are robust. To quantify how cell division is affected by the mechanical and geometrical environment, we present a novel computational mechanical model of cytokinesis, the final phase of cell division. Simulations with the model reproduced experimentally observed furrow dynamics and describe the volume ratio of daughter cells in asymmetric cell divisions, based on the position and orientation of the mitotic spindle. For dividing cells in geometrically confined environments, we show how the orientation of confinement relative to the division axis modulates the volume ratio in asymmetric cell division. Further, we quantified how cortex viscosity and surface tension determine the shape of a dividing cell and govern bubble-instabilities in asymmetric cell division. Finally, we simulated the formation of the three body axes via sequential (a)symmetric divisions up until the six-cell stage of early C. elegans development, which proceeds within the confines of an eggshell. We demonstrate how model input parameters spindle position and orientation provide sufficient information to reliably predict the volume ratio of daughter cells during the cleavage phase of development. However, for egg geometries perturbed by compression, the model predicts that a change in confinement alone is insufficient to explain experimentally observed differences in cell volume. This points to an effect of the compression on the spindle positioning mechanism. Additionally, the model predicts that confinement stabilizes asymmetric cell divisions against bubble-instabilities.

Wrangling Actin Assemblies: Actin Ring Dynamics during Cell Wound Repair

To cope with continuous physiological and environmental stresses, cells of all sizes require an effective wound repair process to seal breaches to their cortex. Once a wound is recognized, the cell must rapidly plug the injury site, reorganize the cytoskeleton and the membrane to pull the wound closed, and finally remodel the cortex to return to homeostasis. Complementary studies using various model organisms have demonstrated the importance and complexity behind the formation and translocation of an actin ring at the wound periphery during the repair process. Proteins such as actin nucleators, actin bundling factors, actin-plasma membrane anchors, and disassembly factors are needed to regulate actin ring dynamics spatially and temporally. Notably, Rho family GTPases have been implicated throughout the repair process, whereas other proteins are required during specific phases. Interestingly, although different models share a similar set of recruited proteins, the way in which they use them to pull the wound closed can differ. Here, we describe what is currently known about the formation, translocation, and remodeling of the actin ring during the cell wound repair process in model organisms, as well as the overall impact of cell wound repair on daily events and its importance to our understanding of certain diseases and the development of therapeutic delivery modalities.

Powering morphogenesis: multiscale challenges at the interface of cell adhesion and the cytoskeleton

Among the defining features of the animal kingdom is the ability of cells to change shape and move. This underlies embryonic and postembryonic development, tissue homeostasis, regeneration, and wound healing. Cell shape change and motility require linkage of the cell's force-generating machinery to the plasma membrane at cell-cell and cell-extracellular matrix junctions. Connections of the actomyosin cytoskeleton to cell-cell adherens junctions need to be both resilient and dynamic, preventing tissue disruption during the dramatic events of embryonic morphogenesis. In the past decade, new insights radically altered the earlier simple paradigm that suggested simple linear linkage via the cadherin-catenin complex as the molecular mechanism of junction-cytoskeleton interaction. In this Perspective we provide a brief overview of our current state of knowledge and then focus on selected examples highlighting what we view as the major unanswered questions in our field and the approaches that offer exciting new insights at multiple scales from atomic structure to tissue mechanics.

Dynamics and Stability of the Contractile Actomyosin Ring in the Cell

Contraction of the cytokinetic ring during cell division leads to physical partitioning of a eukaryotic cell into two daughter cells. This involves flows of actin filaments and myosin motors in the growing membrane interface at the midplane of the dividing cell. Assuming boundary driven alignment of the actomyosin filaments at the inner edge of the interface, we explore how the resulting active stresses influence the flow. Using the continuum gel theory framework, we obtain exact axisymmetric solutions of the dynamical equations. These solutions are consistent with experimental observations on closure rate. Using these solutions, we perform linear stability analysis for the contracting ring under nonaxisymmetric deformations. Our analysis shows that few low wave number modes, which are unstable during onset of the constriction, later on become stable when the ring shrinks to smaller radii, which is a generic feature of actomyosin ring closure. Our theory also captures how the effective tension in the ring decreases with its radius, causing significant slowdown in the contraction process at later times.

Protein friction and filament bending facilitate contraction of disordered actomyosin networks

We use mathematical modeling and computation to investigate how protein friction facilitates contraction of disordered actomyosin networks. We simulate two-dimensional networks using an agent-based model, consisting of a system of force-balance equations for myosin motor proteins and semiflexible actin filaments. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility. Exploiting this, we use repeated simulations of disordered networks to confirm that both protein friction and actin filament bending are required for contraction. We then use simulations of elementary two-filament systems to show that filament bending flexibility can facilitate contraction on the microscopic scale. Finally, we show that actin filament turnover is necessary to sustain contraction and prevent filament aggregation. Simulations with and without turnover also exhibit contractile pulses. However, these pulses are aperiodic, suggesting that periodic pulsation can only arise because of additional regulatory mechanisms or more complex mechanical behavior.

The Ringleaders: Understanding the Apicomplexan Basal Complex Through Comparison to Established Contractile Ring Systems

The actomyosin contractile ring is a key feature of eukaryotic cytokinesis, conserved across many eukaryotic kingdoms. Recent research into the cell biology of the divergent eukaryotic clade Apicomplexa has revealed a contractile ring structure required for asexual division in the medically relevant genera Toxoplasma and Plasmodium; however, the structure of the contractile ring, known as the basal complex in these parasites, remains poorly characterized and in the absence of a myosin II homolog, it is unclear how the force required of a cytokinetic contractile ring is generated. Here, we review the literature on the basal complex in Apicomplexans, summarizing what is known about its formation and function, and attempt to provide possible answers to this question and suggest new avenues of study by comparing the Apicomplexan basal complex to well-studied, established cytokinetic contractile rings and their mechanisms in organisms such as S. cerevisiae and D. melanogaster. We also compare the basal complex to structures formed during mitochondrial and plastid division and cytokinetic mechanisms of organisms beyond the Opisthokonts, considering Apicomplexan diversity and divergence.

Cytoplasm's Got Moves

Cytoplasm is a gel-like crowded environment composed of various macromolecules, organelles, cytoskeletal networks, and cytosol. The structure of the cytoplasm is highly organized and heterogeneous due to the crowding of its constituents and their effective compartmentalization. In such an environment, the diffusive dynamics of the molecules are restricted, an effect that is further amplified by clustering and anchoring of molecules. Despite the crowded nature of the cytoplasm at the microscopic scale, large-scale reorganization of the cytoplasm is essential for important cellular functions, such as cell division and polarization. How such mesoscale reorganization of the cytoplasm is achieved, especially for large cells such as oocytes or syncytial tissues that can span hundreds of micrometers in size, is only beginning to be understood. In this review, we will discuss recent advances in elucidating the molecular, cellular, and biophysical mechanisms by which the cytoskeleton drives cytoplasmic reorganization across different scales, structures, and species.

Reversal of contractility as a signature of self-organization in cytoskeletal bundles

Bundles of cytoskeletal filaments and molecular motors generate motion in living cells, and have internal structures ranging from very organized to apparently disordered. The mechanisms powering the disordered structures are debated, and existing models predominantly predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay between three well-characterized internal dynamical processes in cytoskeletal bundles: filament assembly and disassembly, the attachement-detachment dynamics of motors and that of crosslinking proteins. The resulting self-organization is easily understood in terms of motor and crosslink localization, and allows for an extensive control of the active bundle mechanics, including reversals of the filaments’ apparent velocities and the possibility of generating extension instead of contraction. This reversal mirrors some recent experimental observations, and provides a robust criterion to experimentally elucidate the underpinnings of both actomyosin activity and the dynamics of microtubule/motor assemblies in vitro as well as in diverse intracellular structures ranging from contractile bundles to the mitotic spindle.

Mechanical conditions for stable symmetric cell constriction

Cell constriction is a decisive step for division in many cells. However, its physical pathway remains poorly understood, calling for a quantitative analysis of the forces required in different cytokinetic scenarios. Using a model cell composed by a flexible membrane (actin cortex and cell membrane) that encloses the cytoplasm, we study the mechanical conditions necessary for stable symmetric constriction under radial equatorial forces using analytical and numerical methods. We deduce that stable symmetric constriction requires positive effective spontaneous curvature, while spontaneous constriction requires a spontaneous curvature higher than the characteristic inverse cell size. Surface tension reduction (for example by actin cortex growth and membrane trafficking) increases the stability and spontaneity of cellular constriction. A reduction of external pressure also increases stability and spontaneity. Cells with prolate lobes (elongated cells) require lower stabilization forces than oblate-shaped cells (discocytes). We also show that the stability and spontaneity of symmetric constriction increase as constriction progresses. Our quantitative results settle the physical requirements for stable cytokinesis, defining a quantitative framework to analyze the mechanical role of the different constriction machinery and cytokinetic pathways found in real cells, so contributing to a deeper quantitative understanding of the physical mechanism of the cell division process.

Actin and myosin dynamics are independent during Drosophila embryonic wound repair

Collective cell movements play a central role in embryonic development, tissue repair, and metastatic disease. Cell movements are often coordinated by supracellular networks formed by the cytoskeletal protein actin and the molecular motor nonmuscle myosin II. During wound closure in the embryonic epidermis, the cells around the wound migrate collectively into the damaged region. In Drosophila embryos, mechanical tension stabilizes myosin at the wound edge, facilitating the assembly of a supracellular myosin cable around the wound that coordinates cell migration. Here, we show that actin is also stabilized at the wound edge. However, loss of tension or myosin activity does not affect the dynamics of actin at the wound margin. Conversely, pharmacological stabilization of actin does not affect myosin levels or dynamics around the wound. Together, our data suggest that actin and myosin are independently regulated during embryonic wound closure, thus conferring robustness to the embryonic wound healing response.

Actin Disassembly: How to Contract without Motors?

Contractile actin networks take on various functions in cells. How disordered actin networks contract is still poorly understood. A recent study proposes a contractile mechanism that is driven by actin disassembly and required to prevent chromosome losses in starfish oocytes.

Molecular Mechanism of Cytokinesis

Division of amoebas, fungi, and animal cells into two daughter cells at the end of the cell cycle depends on a common set of ancient proteins, principally actin filaments and myosin-II motors. Anillin, formins, IQGAPs, and many other proteins regulate the assembly of the actin filaments into a contractile ring positioned between the daughter nuclei by different mechanisms in fungi and animal cells. Interactions of myosin-II with actin filaments produce force to assemble and then constrict the contractile ring to form a cleavage furrow. Contractile rings disassemble as they constrict. In some cases, knowledge about the numbers of participating proteins and their biochemical mechanisms has made it possible to formulate molecularly explicit mathematical models that reproduce the observed physical events during cytokinesis by computer simulations.

Molecular Mechanism of Cytokinesis

Division of amoebas, fungi, and animal cells into two daughter cells at the end of the cell cycle depends on a common set of ancient proteins, principally actin filaments and myosin-II motors. Anillin, formins, IQGAPs, and many other proteins regulate the assembly of the actin filaments into a contractile ring positioned between the daughter nuclei by different mechanisms in fungi and animal cells. Interactions of myosin-II with actin filaments produce force to assemble and then constrict the contractile ring to form a cleavage furrow. Contractile rings disassemble as they constrict. In some cases, knowledge about the numbers of participating proteins and their biochemical mechanisms has made it possible to formulate molecularly explicit mathematical models that reproduce the observed physical events during cytokinesis by computer simulations.

Network Contractility During Cytokinesis-from Molecular to Global Views

Cytokinesis is the last stage of cell division, which partitions the mother cell into two daughter cells. It requires the assembly and constriction of a contractile ring that consists of a filamentous contractile network of actin and myosin. Network contractility depends on network architecture, level of connectivity and myosin motor activity, but how exactly is the contractile ring network organized or interconnected and how much it depends on motor activity remains unclear. Moreover, the contractile ring is not an isolated entity; rather, it is integrated into the surrounding cortex. Therefore, the mechanical properties of the cell cortex and cortical behaviors are expected to impact contractile ring functioning. Due to the complexity of the process, experimental approaches have been coupled to theoretical modeling in order to advance its global understanding. While earlier coarse-grained descriptions attempted to provide an integrated view of the process, recent models have mostly focused on understanding the behavior of an isolated contractile ring. Here we provide an overview of the organization and dynamics of the actomyosin network during cytokinesis and discuss existing theoretical models in light of cortical behaviors and experimental evidence from several systems. Our view on what is missing in current models and should be tested in the future is provided.

Mitotic Cell Division in Caenorhabditis elegans

Mitotic cell divisions increase cell number while faithfully distributing the replicated genome at each division. The Caenorhabditis elegans embryo is a powerful model for eukaryotic cell division. Nearly all of the genes that regulate cell division in C. elegans are conserved across metazoan species, including humans. The C. elegans pathways tend to be streamlined, facilitating dissection of the more redundant human pathways. Here, we summarize the virtues of C. elegans as a model system and review our current understanding of centriole duplication, the acquisition of pericentriolar material by centrioles to form centrosomes, the assembly of kinetochores and the mitotic spindle, chromosome segregation, and cytokinesis.

Unite to divide - how models and biological experimentation have come together to reveal mechanisms of cytokinesis

Cytokinesis is the fundamental and ancient cellular process by which one cell physically divides into two. Cytokinesis in animal and fungal cells is achieved by contraction of an actomyosin cytoskeletal ring assembled in the cell cortex, typically at the cell equator. Cytokinesis is essential for the development of fertilized eggs into multicellular organisms and for homeostatic replenishment of cells. Correct execution of cytokinesis is also necessary for genome stability and the evasion of diseases including cancer. Cytokinesis has fascinated scientists for well over a century, but its speed and dynamics make experiments challenging to perform and interpret. The presence of redundant mechanisms is also a challenge to understand cytokinesis, leaving many fundamental questions unresolved. For example, how does a disordered cytoskeletal network transform into a coherent ring? What are the long-distance effects of localized contractility? Here, we provide a general introduction to 'modeling for biologists', and review how agent-based modeling and continuum mechanics modeling have helped to address these questions.

Molecular mechanisms of contractile-ring constriction and membrane trafficking in cytokinesis

In this review, we discuss the molecular mechanisms of cytokinesis from plants to humans, with a focus on contribution of membrane trafficking to cytokinesis. Selection of the division site in fungi, metazoans, and plants is reviewed, as well as the assembly and constriction of a contractile ring in fungi and metazoans. We also provide an introduction to exocytosis and endocytosis, and discuss how they contribute to successful cytokinesis in eukaryotic cells. The conservation in the coordination of membrane deposition and cytoskeleton during cytokinesis in fungi, metazoans, and plants is highlighted.

Elastic capsules at liquid-liquid interfaces

We investigate the deformation of elastic microcapsules adsorbed at liquid-liquid interfaces. An initially spherical elastic capsule at a liquid-liquid interface undergoes circumferential stretching due to the liquid-liquid surface tension and becomes lens- or discus-shaped, depending on its bending rigidity. The resulting elastic capsule deformation is qualitatively similar, but distinct from the deformation of a liquid droplet into a liquid lens at a liquid-liquid interface. We discuss the deformed shapes of droplets and capsules adsorbed at liquid-liquid interfaces for a whole range of different surface elasticities: from droplets (only surface tension) deforming into liquid lenses, droplets with a Hookean membrane (finite stretching modulus, zero bending modulus) deforming into elastic lenses, to microcapsules (finite stretching and bending modulus) deforming into rounded elastic lenses. We calculate capsule shapes at liquid-liquid interfaces numerically using shape equations from nonlinear elastic shell theory. Finally, we present theoretical results for the contact angle (or the capsule height) and the maximal capsule curvature at the three phase contact line. These results can be used to infer information about the elastic moduli from optical measurements. During capsule deformation into a lens-like shape, surface energy of the liquid-liquid interface is converted into elastic energy of the capsule shell giving rise to an overall adsorption energy gain by deformation. Soft hollow capsules exhibit a pronounced increase of the adsorption energy as compared to filled soft particles and, thus, are attractive candidates as foam and emulsion stabilizers.

Actin Assemblies in the Axon Shaft - some Open Questions

The actin cytoskeleton in neurons plays critical roles in axonal growth and synaptic organization. Until recently, most studies on axonal actin were limited to terminal growth cones or synapses, whereas the organization of actin along the shaft of the axon was relatively ignored. However, experiments using super-resolution microscopy and live imaging have revealed previously unknown actin structures along the axonal shaft, such as periodic 'actin rings' circumferentially wrapping underneath the plasma membrane and dynamic actin pools deeper within the axon shaft (termed actin 'hotspots' and 'trails'). In this short review, we highlight some open questions that have surfaced as a direct result of these discoveries.

A positive-feedback-based mechanism for constriction rate acceleration during cytokinesis in Caenorhabditis elegans

To ensure timely cytokinesis, the equatorial actomyosin contractile ring constricts at a relatively constant rate despite its progressively decreasing size. Thus, the per-unit-length constriction rate increases as ring perimeter decreases. To understand this acceleration, we monitored cortical surface and ring component dynamics during the first cytokinesis of the Caenorhabditis elegans embryo. We found that, per unit length, the amount of ring components (myosin, anillin) and the constriction rate increase with parallel exponential kinetics. Quantitative analysis of cortical flow indicated that the cortex within the ring is compressed along the axis perpendicular to the ring, and the per-unit-length rate of cortical compression increases during constriction in proportion to ring myosin. We propose that positive feedback between ring myosin and compression-driven flow of cortex into the ring drives an exponential increase in the per-unit-length amount of ring myosin to maintain a high ring constriction rate and support this proposal with an analytical mathematical model.

Coarse-grained simulations of actomyosin rings point to a nodeless model involving both unipolar and bipolar myosins

Cytokinesis in many eukaryotic cells is orchestrated by a contractile actomyosin ring. While many of the proteins involved are known, the mechanism of constriction remains unclear. Informed by the existing literature and new three-dimensional (3D) molecular details from electron cryotomography, here we develop 3D coarse-grained models of actin filaments, unipolar and bipolar myosins, actin cross-linkers, and membranes and simulate their interactions. Assuming that local force on the membrane results in inward growth of the cell wall, we explored a matrix of possible actomyosin configurations and found that node-based architectures like those presently described for ring assembly result in membrane puckers not seen in electron microscope images of real cells. Instead, the model that best matches data from fluorescence microscopy, electron cryotomography, and biochemical experiments is one in which actin filaments transmit force to the membrane through evenly distributed, membrane-attached, unipolar myosins, with bipolar myosins in the ring driving contraction. While at this point this model is only favored (not proven), the work highlights the power of coarse-grained biophysical simulations to compare complex mechanistic hypotheses.

A disassembly-driven mechanism explains F-actin-mediated chromosome transport in starfish oocytes

While contraction of sarcomeric actomyosin assemblies is well understood, this is not the case for disordered networks of actin filaments (F-actin) driving diverse essential processes in animal cells. For example, at the onset of meiosis in starfish oocytes a contractile F-actin network forms in the nuclear region transporting embedded chromosomes to the assembling microtubule spindle. Here, we addressed the mechanism driving contraction of this 3D disordered F-actin network by comparing quantitative observations to computational models. We analyzed 3D chromosome trajectories and imaged filament dynamics to monitor network behavior under various physical and chemical perturbations. We found no evidence of myosin activity driving network contractility. Instead, our observations are well explained by models based on a disassembly-driven contractile mechanism. We reconstitute this disassembly-based contractile system in silico revealing a simple architecture that robustly drives chromosome transport to prevent aneuploidy in the large oocyte, a prerequisite for normal embryonic development.

Asymmetric Flows in the Intercellular Membrane during Cytokinesis

Eukaryotic cells undergo shape changes during their division and growth. This involves flow of material both in the cell membrane and in the cytoskeletal layer beneath the membrane. Such flows result in redistribution of phospholipid at the cell surface and actomyosin in the cortex. Here we focus on the growth of the intercellular surface during cell division in a Caenorhabditis elegans embryo. The growth of this surface leads to the formation of a double-layer of separating membranes between the two daughter cells. The division plane typically has a circular periphery and the growth starts from the periphery as a membrane invagination, which grows radially inward like the shutter of a camera. The growth is typically not concentric, in the sense that the closing internal ring is located off-center. Cytoskeletal proteins anillin and septin have been found to be responsible for initiating and maintaining the asymmetry of ring closure but the role of possible asymmetry in the material flow into the growing membrane has not been investigated yet. Motivated by experimental evidence of such flow asymmetry, here we explore the patterns of internal ring closure in the growing membrane in response to asymmetric boundary fluxes. We highlight the importance of the flow asymmetry by showing that many of the asymmetric growth patterns observed experimentally can be reproduced by our model, which incorporates the viscous nature of the membrane and contractility of the associated cortex.

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.

Cross-linkers both drive and brake cytoskeletal remodeling and furrowing in cytokinesis

Cell shape changes such as cytokinesis are driven by the actomyosin contractile cytoskeleton. The molecular rearrangements that bring about contractility in nonmuscle cells are currently debated. Specifically, both filament sliding by myosin motors, as well as cytoskeletal cross-linking by myosins and nonmotor cross-linkers, are thought to promote contractility. Here we examined how the abundance of motor and nonmotor cross-linkers affects the speed of cytokinetic furrowing. We built a minimal model to simulate contractile dynamics in the Caenorhabditis elegans zygote cytokinetic ring. This model predicted that intermediate levels of nonmotor cross-linkers are ideal for contractility; in vivo, intermediate levels of the scaffold protein anillin allowed maximal contraction speed. Our model also demonstrated a nonlinear relationship between the abundance of motor ensembles and contraction speed. In vivo, thorough depletion of nonmuscle myosin II delayed furrow initiation, slowed F-actin alignment, and reduced maximum contraction speed, but partial depletion allowed faster-than-expected kinetics. Thus, cytokinetic ring closure is promoted by moderate levels of both motor and nonmotor cross-linkers but attenuated by an over-abundance of motor and nonmotor cross-linkers. Together, our findings extend the growing appreciation for the roles of cross-linkers in cytokinesis and reveal that they not only drive but also brake cytoskeletal remodeling.

Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.

Myosin Clusters of Finite Size Develop Contractile Stress in 1D Random Actin Arrays

Myosin-powered force generation and contraction in nonmuscle cells underlies many cell biological processes and is based on contractility of random actin arrays. This contractility must rely on a microscopic asymmetry, the precise mechanism of which is not completely clear. A number of models of mechanical and structural asymmetries in actomyosin contraction have been posited. Here, we examine a contraction mechanism based on a finite size of myosin clusters and anisotropy of force generation by myosin heads at the ends of the myosin clusters. We use agent-based numerical simulations to demonstrate that if average lengths of actin filaments and myosin clusters are similar, then the proposed microscopic asymmetry leads to effective contraction of random 1D actomyosin arrays. We discuss the model's implication for mechanics of contractile rings and stress fibers.

LET-99 functions in the astral furrowing pathway, where it is required for myosin enrichment in the contractile ring

LET-99 is required for furrowing during cytokinesis in both symmetrically and asymmetrically dividing cells. This function is distinct from the role of LET-99 in spindle positioning with Gα signaling. LET-99 is localized to the furrow, where it acts to promote myosin enrichment.

The anaphase spindle determines the position of the cytokinesis furrow, such that the contractile ring assembles in an equatorial zone between the two spindle poles. Contractile ring formation is mediated by RhoA activation at the equator by the centralspindlin complex and midzone microtubules. Astral microtubules also inhibit RhoA accumulation at the poles. In the Caenorhabditis elegans one-cell embryo, the astral microtubule–dependent pathway requires anillin, NOP-1, and LET-99. LET-99 is well characterized for generating the asymmetric cortical localization of the Gα-dependent force-generating complex that positions the spindle during asymmetric division. However, whether the role of LET-99 in cytokinesis is specific to asymmetric division and whether it acts through Gα to promote furrowing are unclear. Here we show that LET-99 contributes to furrowing in both asymmetrically and symmetrically dividing cells, independent of its function in spindle positioning and Gα regulation. LET-99 acts in a pathway parallel to anillin and is required for myosin enrichment into the contractile ring. These and other results suggest a positive feedback model in which LET-99 localizes to the presumptive cleavage furrow in response to the spindle and myosin. Once positioned there, LET-99 enhances myosin accumulation to promote furrowing in both symmetrically and asymmetrically dividing cells.

Collective cell migration: a physics perspective

Cells have traditionally been viewed either as independently moving entities or as somewhat static parts of tissues. However, it is now clear that in many cases, multiple cells coordinate their motions and move as collective entities. Well-studied examples comprise development events, as well as physiological and pathological situations. Different ex vivo model systems have also been investigated. Several recent advances have taken place at the interface between biology and physics, and have benefitted from progress in imaging and microscopy, from the use of microfabrication techniques, as well as from the introduction of quantitative tools and models. We review these interesting developments in quantitative cell biology that also provide rich examples of collective out-of-equilibrium motion.

Actin turnover maintains actin filament homeostasis during cytokinetic ring contraction

Many cytokinetic actomyosin ring components undergo dynamic turnover, but its function is unclear. Chew et al. show that continuous actin polymerization ensures crucial F-actin homeostasis during ring contraction, without which ring proteins organize into noncontractile clusters.

Cytokinesis in many eukaryotes involves a tension-generating actomyosin-based contractile ring. Many components of actomyosin rings turn over during contraction, although the significance of this turnover has remained enigmatic. Here, using Schizosaccharomyces japonicus, we investigate the role of turnover of actin and myosin II in its contraction. Actomyosin ring components self-organize into ∼1-µm-spaced clusters instead of undergoing full-ring contraction in the absence of continuous actin polymerization. This effect is reversed when actin filaments are stabilized. We tested the idea that the function of turnover is to ensure actin filament homeostasis in a synthetic system, in which we abolished turnover by fixing rings in cell ghosts with formaldehyde. We found that these rings contracted fully upon exogenous addition of a vertebrate myosin. We conclude that actin turnover is required to maintain actin filament homeostasis during ring contraction and that the requirement for turnover can be bypassed if homeostasis is achieved artificially.

Actin fringes of polar cell growth

The eukaryotic actin cytoskeleton is a highly dynamic framework that is involved in many biological processes, such as cell growth, division, morphology, and motility. G-actin polymerizes into microfilaments that associate into bundles, patches, and networks, which, in turn, organize into higher order structures that are fundamental for the course of important physiological events. Actin rings are an example for such higher order actin entities, but this term represents an actually diverse set of subcellular structures that are involved in various processes. This review especially sheds light on a crucial type of non-constricting ring-like actin networks, and categorizes them under the term 'actin fringe'. These 'actin fringes' are visualized as highly dynamic and yet steady structures in the tip of various polarized growing cells. The present comprehensive overview compares the actin fringe characteristics of rapidly elongating pollen tubes with several related actin arrays in other cell types of diverse species. The current state of knowledge about various actin fringe functions is summarized, and the key role of this structure in the polar growth process is discussed.

Antagonistic Behaviors of NMY-1 and NMY-2 Maintain Ring Channels in the C. elegans Gonad

Contractile rings play critical roles in a number of biological processes, including oogenesis, wound healing, and cytokinesis. In many cases, the activity of motor proteins such as nonmuscle myosins is required for appropriate constriction of these contractile rings. In the gonad of the nematode worm Caenorhabditis elegans, ring channels are a specialized form of contractile ring that are maintained at a constant diameter before oogenesis. We propose a model of ring channel maintenance that explicitly incorporates force generation by motor proteins that can act normally or tangentially to the ring channel opening. We find that both modes of force generation are needed to maintain the ring channels. We demonstrate experimentally that the type II myosins NMY-1 and NMY-2 antagonize each other in the ring channels by producing force in perpendicular directions: the experimental depletion of NMY-1/theoretical decrease in orthogonal force allows premature ring constriction and cellularization, whereas the experimental depletion of NMY-2/theoretical decrease in tangential force opens the ring channels and prevents cellularization. Together, our experimental and theoretical results show that both forces, mediated by NMY-1 and NMY-2, are crucial for maintaining the appropriate ring channel diameter and dynamics throughout the gonad.

Cytoskeletal actin dynamics shape a ramifying actin network underpinning immunological synapse formation

T cell activation and especially trafficking of T cell receptor microclusters during immunological synapse formation are widely thought to rely on cytoskeletal remodeling. However, important details on the involvement of actin in the latter transport processes are missing. Using a suite of advanced optical microscopes to analyze resting and activated T cells, we show that, following contact formation with activating surfaces, these cells sequentially rearrange their cortical actin across the entire cell, creating a previously unreported ramifying actin network above the immunological synapse. This network shows all the characteristics of an inward-growing transportation network and its dynamics correlating with T cell receptor rearrangements. This actin reorganization is accompanied by an increase in the nanoscale actin meshwork size and the dynamic adjustment of the turnover times and filament lengths of two differently sized filamentous actin populations, wherein formin-mediated long actin filaments support a very flat and stiff contact at the immunological synapse interface. The initiation of immunological synapse formation, as highlighted by calcium release, requires markedly little contact with activating surfaces and no cytoskeletal rearrangements. Our work suggests that incipient signaling in T cells initiates global cytoskeletal rearrangements across the whole cell, including a stiffening process for possibly mechanically supporting contact formation at the immunological synapse interface as well as a central ramified transportation network apparently directed at the consolidation of the contact and the delivery of effector functions.

Modeling cytokinesis of eukaryotic cells driven by the actomyosin contractile ring

A three-dimensional (3D) hydrodynamic model for cytokinesis of eukaryotic cells is developed, in which we model dynamics of actomyosins in the cell cortex, in particular, along the cytokinetic ring formed in the cortex and in the neighborhood of the cell's division plane explicitly. Specifically, the active force actuated by the actomyosin's activity along the cytokinetic ring is modeled by a surface force whose strength is proportional to the actomyosin concentration while the cell morphology is tracked by a phase field model. The model is then solved in 3D space and time using a finite difference method on graphic processing units. Dynamical morphological patterns of eukaryotic cells during cytokinesis are numerically simulated with the model. These simulated morphological patterns agree quantitatively with experimental observations. Copyright © 2016 John Wiley & Sons, Ltd.

A Combination of Actin Treadmilling and Cross-Linking Drives Contraction of Random Actomyosin Arrays

We investigate computationally the self-organization and contraction of an initially random actomyosin ring. In the framework of a detailed physical model for a ring of cross-linked actin filaments and myosin-II clusters, we derive the force balance equations and solve them numerically. We find that to contract, actin filaments have to treadmill and to be sufficiently cross linked, and myosin has to be processive. The simulations reveal how contraction scales with mechanochemical parameters. For example, they show that the ring made of longer filaments generates greater force but contracts slower. The model predicts that the ring contracts with a constant rate proportional to the initial ring radius if either myosin is released from the ring during contraction and actin filaments shorten, or if myosin is retained in the ring, while the actin filament number decreases. We demonstrate that a balance of actin nucleation and compression-dependent disassembly can also sustain contraction. Finally, the model demonstrates that with time pattern formation takes place in the ring, worsening the contractile process. The more random the actin dynamics are, the higher the contractility will be.

The final cut: cell polarity meets cytokinesis at the bud neck in S. cerevisiae

Cell division is a fundamental but complex process that gives rise to two daughter cells. It includes an ordered set of events, altogether called "the cell cycle", that culminate with cytokinesis, the final stage of mitosis leading to the physical separation of the two daughter cells. Symmetric cell division equally partitions cellular components between the two daughter cells, which are therefore identical to one another and often share the same fate. In many cases, however, cell division is asymmetrical and generates two daughter cells that differ in specific protein inheritance, cell size, or developmental potential. The budding yeast Saccharomyces cerevisiae has proven to be an excellent system to investigate the molecular mechanisms governing asymmetric cell division and cytokinesis. Budding yeast is highly polarized during the cell cycle and divides asymmetrically, producing two cells with distinct sizes and fates. Many components of the machinery establishing cell polarization during budding are relocalized to the division site (i.e., the bud neck) for cytokinesis. In this review we recapitulate how budding yeast cells undergo polarized processes at the bud neck for cell division.

Still and rotating myosin clusters determine cytokinetic ring constriction

The cytokinetic ring is essential for separating daughter cells during division. It consists of actin filaments and myosin motors that are generally assumed to organize as sarcomeres similar to skeletal muscles. However, direct evidence is lacking. Here we show that the internal organization and dynamics of rings are different from sarcomeres and distinct in different cell types. Using micro-cavities to orient rings in single focal planes, we find in mammalian cells a transition from a homogeneous distribution to a periodic pattern of myosin clusters at the onset of constriction. In contrast, in fission yeast, myosin clusters rotate prior to and during constriction. Theoretical analysis indicates that both patterns result from acto-myosin self-organization and reveals differences in the respective stresses. These findings suggest distinct functional roles for rings: contraction in mammalian cells and transport in fission yeast. Thus self-organization under different conditions may be a generic feature for regulating morphogenesis in vivo.

A theoretical model of cytokinesis implicates feedback between membrane curvature and cytoskeletal organization in asymmetric cytokinetic furrowing

Furrow ingression is asymmetric in cytokinesis in the Caenorhabditis elegans zygote. A combination of quantitative high-resolution live-cell microscopy and theoretical modeling revealed a mechanistic basis for asymmetry: feedback among membrane curvature, cytoskeletal alignment, and contractility. The model also suggests that asymmetry promotes energy efficiency.

During cytokinesis, the cell undergoes a dramatic shape change as it divides into two daughter cells. Cell shape changes in cytokinesis are driven by a cortical ring rich in actin filaments and nonmuscle myosin II. The ring closes via actomyosin contraction coupled with actin depolymerization. Of interest, ring closure and hence the furrow ingression are nonconcentric (asymmetric) within the division plane across Metazoa. This nonconcentricity can occur and persist even without preexisting asymmetric cues, such as spindle placement or cellular adhesions. Cell-autonomous asymmetry is not explained by current models. We combined quantitative high-resolution live-cell microscopy with theoretical modeling to explore the mechanistic basis for asymmetric cytokinesis in the Caenorhabditis elegans zygote, with the goal of uncovering basic principles of ring closure. Our theoretical model suggests that feedback among membrane curvature, cytoskeletal alignment, and contractility is responsible for asymmetric cytokinetic furrowing. It also accurately predicts experimental perturbations of conserved ring proteins. The model further suggests that curvature-mediated filament alignment speeds up furrow closure while promoting energy efficiency. Collectively our work underscores the importance of membrane–cytoskeletal anchoring and suggests conserved molecular mechanisms for this activity.

Actomyosin ring driven cytokinesis in budding yeast

Cytokinesis is the final process in the cell cycle that physically divides one cell into two. In budding yeast, cytokinesis is driven by a contractile actomyosin ring (AMR) and the simultaneous formation of a primary septum, which serves as template for cell wall deposition. AMR assembly, constriction, primary septum formation and cell wall deposition are successive processes and tightly coupled to cell cycle progression to ensure the correct distribution of genetic material and cell organelles among the two rising cells prior to cell division. The role of the AMR in cytokinesis and the molecular mechanisms that drive AMR constriction and septation are the focus of current research. This review summarizes the recent progresses in our understanding of how budding yeast cells orchestrate the multitude of molecular mechanisms that control AMR driven cytokinesis in a spatio-temporal manner to achieve an error free cell division.

Constriction model of actomyosin ring for cytokinesis by fission yeast using a two-state sliding filament mechanism

We developed a model describing the structure and contractile mechanism of the actomyosin ring in fission yeast, Schizosaccharomyces pombe. The proposed ring includes actin, myosin, and α-actinin, and is organized into a structure similar to that of muscle sarcomeres. This structure justifies the use of the sliding-filament mechanism developed by Huxley and Hill, but it is probably less organized relative to that of muscle sarcomeres. Ring contraction tension was generated via the same fundamental mechanism used to generate muscle tension, but some physicochemical parameters were adjusted to be consistent with the proposed ring structure. Simulations allowed an estimate of ring constriction tension that reproduced the observed ring constriction velocity using a physiologically possible, self-consistent set of parameters. Proposed molecular-level properties responsible for the thousand-fold slower constriction velocity of the ring relative to that of muscle sarcomeres include fewer myosin molecules involved, a less organized contractile configuration, a low α-actinin concentration, and a high resistance membrane tension. Ring constriction velocity is demonstrated as an exponential function of time despite a near linear appearance. We proposed a hypothesis to explain why excess myosin heads inhibit constriction velocity rather than enhance it. The model revealed how myosin concentration and elastic resistance tension are balanced during cytokinesis in S. pombe.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

Morphogenesis of the mouse neural plate depends on distinct roles of cofilin 1 in apical and basal epithelial domains

The genetic control of mammalian epithelial polarity and dynamics can be studied in vivo at cellular resolution during morphogenesis of the mouse neural tube. The mouse neural plate is a simple epithelium that is transformed into a columnar pseudostratified tube over the course of ∼ 24 h. Apical F-actin is known to be important for neural tube closure, but the precise roles of actin dynamics in the neural epithelium are not known. To determine how the organization of the neural epithelium and neural tube closure are affected when actin dynamics are blocked, we examined the cellular basis of the neural tube closure defect in mouse mutants that lack the actin-severing protein cofilin 1 (CFL1). Although apical localization of the adherens junctions, the Par complex, the Crumbs complex and SHROOM3 is normal in the mutants, CFL1 has at least two distinct functions in the apical and basal domains of the neural plate. Apically, in the absence of CFL1 myosin light chain does not become phosphorylated, indicating that CFL1 is required for the activation of apical actomyosin required for neural tube closure. On the basal side of the neural plate, loss of CFL1 has the opposite effect on myosin: excess F-actin and myosin accumulate and the ectopic myosin light chain is phosphorylated. The basal accumulation of F-actin is associated with the assembly of ectopic basal tight junctions and focal disruptions of the basement membrane, which eventually lead to a breakdown of epithelial organization.

Cytokinetic abscission: molecular mechanisms and temporal control

Cytokinesis mediates the physical separation of dividing cells after chromosome segregation. In animal cell cytokinesis, a contractile ring, mainly composed of actin and myosin filaments, ingresses a cleavage furrow midway between the two spindle poles. A distinct machinery, involving the endosomal sorting complex required for transport III (ESCRT-III), subsequently splits the plasma membrane of nascent daughter cells in a process termed abscission. Here, we provide a brief overview of early cytokinesis events in animal cells and then cover in depth recently emerging models for the assembly and function of the abscission machinery and its temporal coordination with chromosome segregation.

Synthetic polyamines: new compounds specific to actin dynamics for mammalian cell and fission yeast

Actin is a major actor in the determination of cell shape. On the one hand, site-directed assembly/disassembly cycles of actin filaments drive protrusive force leading to lamellipodia and filopodia dynamics. Force produced by actin similarly contributes in membrane scission in endocytosis or Golgi remodeling. On the other hand, cellular processes like adhesion, immune synapse, cortex dynamics or cytokinesis are achieved by combining acto-myosin contractility and actin assembly in a complex and not fully understood manner. New chemical compounds are therefore needed to disentangle acto-myosin and actin dynamics. We have found that synthetic, cell permeant, short polyamines are promising new actin regulators in this context. They generate growth and stabilization of lamellipodia within minutes by slowing down the actin assembly/disassembly cycle and facilitating nucleation. We now report that these polyamines also slow down cytokinetic ring closure in fission yeast. This shows that these synthetic compounds are active also in yeasts, and these experiments specifically highlight that actin depolymerization is involved in the ring closure. Thus, synthetic polyamines appear to be potentially powerful agents in a quantitative approach to the role of actin in complex processes in cell biology, developmental biology and potentially cancer research.