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

Anillin mediates unilateral furrowing during cytokinesis by limiting RhoA binding to its effectors

During unilateral furrow ingression, one side of the cytokinetic ring (leading edge) ingresses before the opposite side (lagging edge). Anillin mediates unilateral furrowing during cytokinesis in the one-cell C. elegans zygote by limiting myosin II accumulation in the ring. Here, we address the role of anillin in this process and show that anillin inhibits not only the accumulation of myosin II but also of other RhoA effectors by binding and blocking the RhoA effector site. The interaction between the anillin's RhoA-binding domain (RBD) and active RhoA is enhanced by the disordered linker region and differentially regulated at the leading and lagging edge, which together results in asymmetric RhoA signaling and accumulation of myosin II. In summary, we discover a RhoA GEF- and GAP-independent mechanism, where RhoA activity is limited by anillin binding to the RhoA effector site. Spatial fine-tuning of anillin's inhibitory role on RhoA signaling enables unilateral furrow ingression and contributes to animal development.

Dynamic Plasma Membrane Topography Linked With Arp2/3 Actin Network Induction During Cell Shape Change

Recent studies show the importance of mesoscale changes to plasma membrane (PM) topography during cell shape change. Local folding and flattening of the cell surface is mechanosensitive, changing in response to both microenvironment structural elements and intracellular cytoskeletal activities. These topography changes elicit local mechanical signaling events that act in conjunction with molecular signal transduction pathways to remodel the cell cortex. Experimental manipulations of local PM curvature show its sufficiency for recruiting Arp2/3 actin network induction pathways. Additionally, studies of diverse cell shape changes-ranging from neutrophil migration to early Drosophila embryo cleavage to neural stem cell asymmetric division-show that local generation of PM folding is linked with local Arp2/3 actin network induction, which then remodels the PM topography during dynamic control of cell structure. These examples are reviewed in detail, together with known and potential causes of PM topography changes, downstream effects, and higher-order feedback.

Subcellular context-specific tuning of actomyosin ring contractility within a common cytoplasm

The non-muscle actomyosin cytoskeleton generates contractile force through the dynamic rearrangement of its constituent parts. Actomyosin rings are a specialization of the non-muscle actomyosin cytoskeleton that drive cell shape changes during division, wound healing, and other events. Contractile rings throughout phylogeny and in a range of cellular contexts are built from conserved components including non-muscle myosin II (NMMII), actin filaments (F-actin), and crosslinking proteins. However, it is unknown whether diverse actomyosin rings close via a single unifying mechanism. To explore how contractile forces are generated by actomyosin rings, we studied three instances of ring closure within the common cytoplasm of the C. elegans oogenic germline: mitotic cytokinesis of germline stem cells (GSCs), apoptosis of meiotic compartments, and cellularization of oocytes. We found that each ring type closed with unique kinetics, protein density and abundance dynamics. These measurements suggested that the mechanism of contractile force generation varied across the subcellular contexts. Next, we formulated a physical model that related the forces generated by filament-filament interactions to the material properties of these rings that dictate the kinetics of their closure. Using this framework, we related the density of conserved cytoskeletal proteins anillin and NMMII to the kinematics of ring closure. We fitted model rings to in situ measurements to estimate parameters that are currently experimentally inaccessible, such as the asymmetric distribution of protein along the length of F-actin, which occurs naturally due to differences in the dimensions of the crosslinker and NMMII filaments. Our work predicted that the role of NMMII varies across these ring types, due in part to its distribution along F-actin and motoring. Our model also predicted that the degree of contractility and the impact of ring material properties on contractility differs among ring types.

Mechanical and biochemical feedback combine to generate complex contractile oscillations in cytokinesis

The actomyosin cortex is an active material that generates force to drive shape changes via cytoskeletal remodeling. Cytokinesis is the essential cell division event during which a cortical actomyosin ring closes to separate two daughter cells. Our active gel theory predicted that actomyosin systems controlled by a biochemical oscillator and experiencing mechanical strain would exhibit complex spatiotemporal behavior. To test whether active materials in vivo exhibit spatiotemporally complex kinetics, we imaged the C. elegans embryo with unprecedented temporal resolution and discovered that sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Contractile oscillations exhibited a range of periodicities, including those much longer periods than the timescale of RhoA pulses, which was shorter in cytokinesis than in any other biological context. Modifying mechanical feedback in vivo or in silico revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Fast local ring ingression occurs where speed oscillations have long periods, likely due to increased local stresses and, therefore, mechanical feedback. Fast ingression also occurs where material turnover is high, in vivo and in silico. We propose that downstream of initiation by pulsed RhoA activity, mechanical feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and, therefore, makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows for sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Thus, like biochemical feedback, mechanical feedback affords active materials responsiveness and robustness.

Perspectives on Principles of Cellular Behavior from the Biophysics of Protists

Cells are the fundamental unit of biological organization. Although it may be easy to think of them as little more than the simple building blocks of complex organisms such as animals, single cells are capable of behaviors of remarkable apparent sophistication. This is abundantly clear when considering the diversity of form and function among the microbial eukaryotes, the protists. How might we navigate this diversity in the search for general principles of cellular behavior? Here, we review cases in which the intensive study of protists from the perspective of cellular biophysics has driven insight into broad biological questions of morphogenesis, navigation and motility, and decision making. We argue that applying such approaches to questions of evolutionary cell biology presents rich, emerging opportunities. Integrating and expanding biophysical studies across protist diversity, exploiting the unique characteristics of each organism, will enrich our understanding of general underlying principles.

Mechanical positive feedback and biochemical negative feedback combine to generate complex contractile oscillations in cytokinesis

Contractile force generation by the cortical actomyosin cytoskeleton is essential for a multitude of biological processes. The actomyosin cortex behaves as an active material that drives local and large-scale shape changes via cytoskeletal remodeling in response to biochemical cues and feedback loops. Cytokinesis is the essential cell division event during which a cortical actomyosin ring generates contractile force to change cell shape and separate two daughter cells. Our recent work with active gel theory predicts that actomyosin systems under the control of a biochemical oscillator and experiencing mechanical strain will exhibit complex spatiotemporal behavior, but cytokinetic contractility was thought to be kinetically simple. To test whether active materials in vivo exhibit spatiotemporally complex kinetics, we used 4-dimensional imaging with unprecedented temporal resolution and discovered sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Quantification of ingression speed oscillations revealed wide ranges of oscillation period and amplitude. In the cytokinetic ring, activity of the master regulator RhoA pulsed with a timescale of approximately 20 seconds, shorter than that reported for any other biological context. Contractility oscillated with 20-second periodicity and with much longer periods. A combination of in vivo and in silico approaches to modify mechanical feedback revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Effective local ring ingression is characterized by slower speed oscillations, likely due to increased local stresses and therefore mechanical feedback. Fast ingression also occurs where material turnover is high, in vivo and in silico . We propose that downstream of initiation by pulsed RhoA activity, mechanical positive feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and therefore makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Our work demonstrates that while biochemical feedback loops afford systems responsiveness and robustness, mechanical feedback must also be considered to describe and understand the behaviors of active materials in vivo .

Dynamics of actomyosin filaments in the contractile ring revealed by ultrastructural analysis

Cytokinesis, the final process of cell division, involves the accumulation of actin and myosin II filaments at the cell's equator, forming a contractile ring that facilitates the division into two daughter cells. While light microscopy has provided valuable insights into the molecular mechanism of this process, it has limitations in examining individual filaments in vivo. In this study, we utilized transmission electron microscopy to observe actin and myosin II filaments in the contractile rings of dividing Dictyostelium cells. To synchronize cytokinesis, we developed a novel method that allowed us to visualize dividing cells undergoing cytokinesis with a frequency as high as 18%. This improvement enabled us to examine the lengths and alignments of individual filaments within the contractile rings. As the furrow constricted, the length of actin filaments gradually decreased. Moreover, both actin and myosin II filaments reoriented perpendicularly to the long axis during furrow constriction. Through experiments involving myosin II null cells, we discovered that myosin II plays a role in regulating both the lengths and alignments of actin filaments. Additionally, dynamin-like protein A was found to contribute to regulating the length of actin filaments, while cortexillins were involved in regulating their alignment.

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.

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.

Diversity is the spice of life: An overview of how cytokinesis regulation varies with cell type

Cytokinesis is required to physically cleave a cell into two daughters at the end of mitosis. Decades of research have led to a comprehensive understanding of the core cytokinesis machinery and how it is regulated in animal cells, however this knowledge was generated using single cells cultured in vitro, or in early embryos before tissues develop. This raises the question of how cytokinesis is regulated in diverse animal cell types and developmental contexts. Recent studies of distinct cell types in the same organism or in similar cell types from different organisms have revealed striking differences in how cytokinesis is regulated, which includes different threshold requirements for the structural components and the mechanisms that regulate them. In this review, we highlight these differences with an emphasis on pathways that are independent of the mitotic spindle, and operate through signals associated with the cortex, kinetochores, or chromatin.

Cytokinetic diversity in mammalian cells is revealed by the characterization of endogenous anillin, Ect2 and RhoA

Cytokinesis is required to physically separate the daughter cells at the end of mitosis. This crucial process requires the assembly and ingression of an actomyosin ring, which must occur with high fidelity to avoid aneuploidy and cell fate changes. Most of our knowledge of mammalian cytokinesis was generated using over-expressed transgenes in HeLa cells. Over-expression can introduce artefacts, while HeLa are cancerous human cells that have lost their epithelial identity, and the mechanisms controlling cytokinesis in these cells could be vastly different from other cell types. Here, we tagged endogenous anillin, Ect2 and RhoA with mNeonGreen and characterized their localization during cytokinesis for the first time in live human cells. Comparing anillin localization in multiple cell types revealed cytokinetic diversity with differences in the duration and symmetry of ring closure, and the timing of cortical recruitment. Our findings show that the breadth of anillin correlates with the rate of ring closure, and support models where cell size or ploidy affects the cortical organization, and intrinsic mechanisms control the symmetry of ring closure. This work highlights the need to study cytokinesis in more diverse cell types, which will be facilitated by the reagents generated for this study.

Membrane curvature as a signal to ensure robustness of diverse cellular processes

An increasing corpus of research has demonstrated that membrane shape, generated either by the external environment of the cell or by intrinsic mechanisms such as cytokinesis and vesicle or organelle formation, is an important parameter in the control of diverse cellular processes. In this review we discuss recent findings that demonstrate how membrane curvature (from nanometer to micron length-scales) alters protein function. We describe an expanding toolkit for experimentally modulating membrane curvature to reveal effects on protein function, and discuss how membrane curvature - far from being a passive consequence of the physical environment and the internal protein activity of a cell - is an important signal that controls protein affinity and enzymatic activity to ensure robust forward progression of key processes within the cell.

Symmetry-breaking of animal cytokinesis

Cytokinesis is a mechanism that separates dividing cells via constriction of a supramolecular structure, the contractile ring. In animal cells, three modes of symmetry-breaking of cytokinesis result in unilateral cytokinesis, asymmetric cell division, and oriented cell division. Each mode of cytokinesis plays a significant role in tissue patterning and morphogenesis by the mechanisms that control the orientation and position of the contractile ring relative to the body axis. Despite its significance, the mechanisms involved in the symmetry-breaking of cytokinesis remain unclear in many cell types. Classical embryologists have identified that the geometric relationship between the mitotic spindle and cell cortex induces cytokinesis asymmetry; however, emerging evidence suggests that a concerted flow of compressional cell-cortex materials (cortical flow) is a spindle-independent driving force in spatial cytokinesis control. This review provides an overview of both classical and emerging mechanisms of cytokinesis asymmetry and their roles in animal development.

Filament-guided filament assembly provides structural memory of filament alignment during cytokinesis

During cytokinesis, animal cells rapidly remodel the equatorial cortex to build an aligned array of actin filaments called the contractile ring. Local reorientation of filaments by active equatorial compression is thought to underlie the emergence of filament alignment during ring assembly. Here, combining single molecule analysis and modeling in one-cell C. elegans embryos, we show that filaments turnover is far too fast for reorientation of individual filaments by equatorial compression to explain the observed alignment, even if favorably oriented filaments are selectively stabilized. By tracking single formin/CYK-1::GFP particles to monitor local filament assembly, we identify a mechanism that we call filament-guided filament assembly (FGFA), in which existing filaments serve as templates to orient the growth of new filaments. FGFA sharply increases the effective lifetime of filament orientation, providing structural memory that allows cells to build highly aligned filament arrays in response to equatorial compression, despite rapid turnover of individual filaments.

More than just a barrier: using physical models to couple membrane shape to cell function

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

Going with the flow: insights from Caenorhabditis elegans zygote polarization

Cell polarity is the asymmetric distribution of cellular components along a defined axis. Polarity relies on complex signalling networks between conserved patterning proteins, including the PAR (partitioning defective) proteins, which become segregated in response to upstream symmetry breaking cues. Although the mechanisms that drive the asymmetric localization of these proteins are dependent upon cell type and context, in many cases the regulation of actomyosin cytoskeleton dynamics is central to the transport, recruitment and/or stabilization of these polarity effectors into defined subcellular domains. The transport or advection of PAR proteins by an actomyosin flow was first observed in the Caenorhabditis elegans zygote more than a decade ago. Since then a multifaceted approach, using molecular methods, high-throughput screens, and biophysical and computational models, has revealed further aspects of this flow and how polarity regulators respond to and modulate it. Here, we review recent findings on the interplay between actomyosin flow and the PAR patterning networks in the polarization of the C. elegans zygote. We also discuss how these discoveries and developed methods are shaping our understanding of other flow-dependent polarizing systems. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Animal Cell Cytokinesis: The Rho-Dependent Actomyosin-Anilloseptin Contractile Ring as a Membrane Microdomain Gathering, Compressing, and Sorting Machine

Cytokinesis is the last step of cell division that partitions the cellular organelles and cytoplasm of one cell into two. In animal cells, cytokinesis requires Rho-GTPase-dependent assembly of F-actin and myosin II (actomyosin) to form an equatorial contractile ring (CR) that bisects the cell. Despite 50 years of research, the precise mechanisms of CR assembly, tension generation and closure remain elusive. This hypothesis article considers a holistic view of the CR that, in addition to actomyosin, includes another Rho-dependent cytoskeletal sub-network containing the scaffold protein, Anillin, and septin filaments (collectively termed anillo-septin). We synthesize evidence from our prior work in Drosophila S2 cells that actomyosin and anillo-septin form separable networks that are independently anchored to the plasma membrane. This latter realization leads to a simple conceptual model in which CR assembly and closure depend upon the micro-management of the membrane microdomains to which actomyosin and anillo-septin sub-networks are attached. During CR assembly, actomyosin contractility gathers and compresses its underlying membrane microdomain attachment sites. These microdomains resist this compression, which builds tension. During CR closure, membrane microdomains are transferred from the actomyosin sub-network to the anillo-septin sub-network, with which they flow out of the CR as it advances. This relative outflow of membrane microdomains regulates tension, reduces the circumference of the CR and promotes actomyosin disassembly all at the same time. According to this hypothesis, the metazoan CR can be viewed as a membrane microdomain gathering, compressing and sorting machine that intrinsically buffers its own tension through coordination of actomyosin contractility and anillo-septin-membrane relative outflow, all controlled by Rho. Central to this model is the abandonment of the dogmatic view that the plasma membrane is always readily deformable by the underlying cytoskeleton. Rather, the membrane resists compression to build tension. The notion that the CR might generate tension through resistance to compression of its own membrane microdomain attachment sites, can account for numerous otherwise puzzling observations and warrants further investigation using multiple systems and methods.

Stem cell niche exit in C. elegans via orientation and segregation of daughter cells by a cryptic cell outside the niche

Stem cells reside in and rely upon their niche to maintain stemness but must balance self-renewal with the production of daughters that leave the niche to differentiate. We discovered a mechanism of stem cell niche exit in the canonical C. elegans distal tip cell (DTC) germ stem cell niche mediated by previously unobserved, thin, membranous protrusions of the adjacent somatic gonad cell pair (Sh1). A disproportionate number of germ cell divisions were observed at the DTC-Sh1 interface. Stem-like and differentiating cell fates segregated across this boundary. Spindles polarized, pairs of daughter cells oriented between the DTC and Sh1, and Sh1 grew over the Sh1-facing daughter. Impeding Sh1 growth by RNAi to cofilin and Arp2/3 perturbed the DTC-Sh1 interface, reduced germ cell proliferation, and shifted a differentiation marker. Because Sh1 membrane protrusions eluded detection for decades, it is possible that similar structures actively regulate niche exit in other systems.

Novel cytokinetic ring components drive negative feedback in cortical contractility

Actomyosin cortical contractility drives many cell shape changes including cytokinetic furrowing. While positive regulation of contractility is well characterized, counterbalancing negative regulation and mechanical brakes are less well understood. The small GTPase RhoA is a central regulator, activating cortical actomyosin contractility during cytokinesis and other events. Here we report how two novel cytokinetic ring components, GCK-1 (germinal center kinase-1) and CCM-3 (cerebral cavernous malformations-3), participate in a negative feedback loop among RhoA and its cytoskeletal effectors to inhibit contractility. GCK-1 and CCM-3 are recruited by active RhoA and anillin to the cytokinetic ring, where they in turn limit RhoA activity and contractility. This is evidenced by increased RhoA activity, anillin and nonmuscle myosin II in the cytokinetic ring, and faster cytokinetic furrowing, following depletion of GCK-1 or CCM-3. GCK-1 or CCM-3 depletion also reduced RGA-3 levels in pulses and increased baseline RhoA activity and pulsed contractility during zygote polarization. Together, our results suggest that GCK-1 and CCM-3 regulate cortical actomyosin contractility via negative feedback. These findings have implications for the molecular and cellular mechanisms of cerebral cavernous malformation pathologies.

Force Production by a Bundle of Growing Actin Filaments Is Limited by Its Mechanical Properties

Bundles of actin filaments are central to a large variety of cellular structures such as filopodia, stress fibers, cytokinetic rings, and focal adhesions. The mechanical properties of these bundles are critical for proper force transmission and force bearing. Previous mathematical modeling efforts have focused on bundles' rigidity and shape. However, it remains unknown how bundle length and buckling are controlled by external physical factors. In this work, we present a biophysical model for dynamic bundles of actin filaments submitted to an external load. In combination with in vitro motility assays of beads coated with formins, our model allowed us to characterize conditions for bead movement and bundle buckling. From the deformation profiles, we determined key biophysical properties of tethered actin bundles such as their rigidity and filament density.

Classical and Emerging Regulatory Mechanisms of Cytokinesis in Animal Cells

The primary goal of cytokinesis is to produce two daughter cells, each having a full set of chromosomes. To achieve this, cells assemble a dynamic structure between segregated sister chromatids called the contractile ring, which is made up of filamentous actin, myosin-II, and other regulatory proteins. Constriction of the actomyosin ring generates a cleavage furrow that divides the cytoplasm to produce two daughter cells. Decades of research have identified key regulators and underlying molecular mechanisms; however, many fundamental questions remain unanswered and are still being actively investigated. This review summarizes the key findings, computational modeling, and recent advances in understanding of the molecular mechanisms that control the formation of the cleavage furrow and cytokinesis.

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.

A Cdc42 GEF, Gef1, through endocytosis organizes F-BAR Cdc15 along the actomyosin ring and promotes concentric furrowing

During cytokinesis, fission yeast coordinates actomyosin ring constriction with septum ingression, resulting in concentric furrow formation by a poorly defined mechanism. We report that Schizosaccharomyces pombe cells lacking the Cdc42 activator Gef1, combined with an activated allele of the formin, Cdc12, display non-concentric furrowing. Non-concentrically furrowing cells display uneven distribution of the scaffold Cdc15 along the ring. This suggests that, after ring assembly, uniform Cdc15 distribution along the ring enables proper furrow formation. We find that, after assembly, Cdc15 is recruited to the ring in an Arp2/3 complex-dependent manner and is decreased in the activated cdc12 mutant. Cdc15 at cortical endocytic patches shows increased levels and extended lifetimes in gef1 and activated cdc12 mutants. We hypothesize endocytosis helps recruit Cdc15 to assembled rings; uneven Cdc15 distribution at the ring occurs when endocytic patches contain increased Cdc15 levels and the patch-association rate is slow. Based on this, we developed a mathematical model that captures experimentally observed Cdc15 distributions along the ring. We propose that, at the ring, Gef1 and endocytic events promote uniform Cdc15 organization to enable proper septum ingression and concentric furrow formation.

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.

Mechanisms of contractile ring tension production and constriction

The contractile ring is a remarkable tension-generating cellular machine that constricts and divides cells into two during cytokinesis, the final stage of the cell cycle. Since the ring's discovery, the parallels with muscle have been emphasized. Both are contractile actomyosin machineries, and long ago, a muscle-like sliding filament mechanism was proposed for the ring. This review focuses on the mechanisms that generate ring tension and constrict contractile rings. The emphasis is on fission yeast, whose contractile ring is sufficiently well characterized that realistic mathematical models are feasible, and possible lessons from fission yeast that may apply to animal cells are discussed. Recent discoveries relevant to the organization in fission yeast rings suggest a stochastic steady-state version of the classic sliding filament mechanism for tension. The importance of different modes of anchoring for tension production and for organizational stability of constricting rings is discussed. Possible mechanisms are discussed that set the constriction rate and enable the contractile ring to meet the technical challenge of maintaining structural integrity and tension-generating capacity while continuously disassembling throughout constriction.

Regulation and Assembly of Actomyosin Contractile Rings in Cytokinesis and Cell Repair

Cytokinesis and single-cell wound repair both involve contractile assemblies of filamentous actin (F-actin) and myosin II organized into characteristic ring-like arrays. The assembly of these actomyosin contractile rings (CRs) is specified spatially and temporally by small Rho GTPases, which trigger local actin polymerization and myosin II contractility via a variety of downstream effectors. We now have a much clearer view of the Rho GTPase signaling cascade that leads to the formation of CRs, but some factors involved in CR positioning, assembly, and function remain poorly understood. Recent studies show that this regulation is multifactorial and goes beyond the long-established Ca²⁺ -dependent processes. There is substantial evidence that the Ca²⁺ -independent changes in cell shape, tension, and plasma membrane composition that characterize cytokinesis and single-cell wound repair also regulate CR formation. Elucidating the regulation and mechanistic properties of CRs is important to our understanding of basic cell biology and holds potential for therapeutic applications in human disease. In this review, we present a primer on the factors influencing and regulating CR positioning, assembly, and contraction as they occur in a variety of cytokinetic and single-cell wound repair models. Anat Rec, 301:2051-2066, 2018. © 2018 Wiley Periodicals, Inc.

The ARP2/3 complex prevents excessive formin activity during cytokinesis

Cytokinesis completes cell division by constriction of an actomyosin contractile ring that separates the two daughter cells. Here we use the early Caenorhabditis elegans embryo to explore how the actin filament network in the ring and the surrounding cortex is regulated by the single cytokinesis formin CYK-1 and the ARP2/3 complex, which nucleate nonbranched and branched filaments, respectively. We show that CYK-1 and the ARP2/3 complex are the predominant F-actin nucleators responsible for generating distinct cortical F-actin architectures and that depletion of either nucleator affects the kinetics of cytokinesis. CYK-1 is critical for normal F-actin levels in the contractile ring, and acute inhibition of CYK-1 after furrow ingression slows ring constriction rate, suggesting that CYK-1 activity is required throughout ring constriction. Surprisingly, although the ARP2/3 complex does not localize in the contractile ring, depletion of the ARP2 subunit or treatment with ARP2/3 complex inhibitor delays contractile ring formation and constriction. We present evidence that the delays are due to an excess in formin-nucleated cortical F-actin, suggesting that the ARP2/3 complex negatively regulates CYK-1 activity. We conclude that the kinetics of cytokinesis are modulated by interplay between the two major actin filament nucleators.

How cells sense their own shape - mechanisms to probe cell geometry and their implications in cellular organization and function

Cells come in a variety of shapes that most often underlie their functions. Regulation of cell morphogenesis implies that there are mechanisms for shape sensing that still remain poorly appreciated. Global and local cell geometry features, such as aspect ratio, size or membrane curvature, may be probed by intracellular modules, such as the cytoskeleton, reaction-diffusion systems or molecular complexes. In multicellular tissues, cell shape emerges as an important means to transduce tissue-inherent chemical and mechanical cues into intracellular organization. One emergent paradigm is that cell-shape sensing is most often based upon mechanisms of self-organization, rather than determinism. Here, we review relevant work that has elucidated some of the core principles of how cellular geometry may be conveyed into spatial information to guide processes, such as polarity, signaling, morphogenesis and division-plane positioning.

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.

Cytokinesis in vertebrate cells initiates by contraction of an equatorial actomyosin network composed of randomly oriented filaments

The actomyosin ring generates force to ingress the cytokinetic cleavage furrow in animal cells, yet its filament organization and the mechanism of contractility is not well understood. We quantified actin filament order in human cells using fluorescence polarization microscopy and found that cleavage furrow ingression initiates by contraction of an equatorial actin network with randomly oriented filaments. The network subsequently gradually reoriented actin filaments along the cell equator. This strictly depended on myosin II activity, suggesting local network reorganization by mechanical forces. Cortical laser microsurgery revealed that during cytokinesis progression, mechanical tension increased substantially along the direction of the cell equator, while the network contracted laterally along the pole-to-pole axis without a detectable increase in tension. Our data suggest that an asymmetric increase in cortical tension promotes filament reorientation along the cytokinetic cleavage furrow, which might have implications for diverse other biological processes involving actomyosin rings.

Nine unanswered questions about cytokinesis

Experiments on model systems have revealed that cytokinesis in cells with contractile rings (amoebas, fungi, and animals) depends on shared molecular mechanisms in spite of some differences that emerged during a billion years of divergent evolution. Understanding these fundamental mechanisms depends on identifying the participating proteins and characterizing the mechanisms that position the furrow, assemble the contractile ring, anchor the ring to the plasma membrane, trigger ring constriction, produce force to form a furrow, disassemble the ring, expand the plasma membrane in the furrow, and separate the daughter cell membranes. This review reveals that fascinating questions remain about each step.

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.

General neck condition for the limit shape of budding vesicles

The shape equation and linking conditions for a vesicle with two phase domains are derived. We refine the conjecture on the general neck condition for the limit shape of a budding vesicle proposed by Jülicher and Lipowsky [Phys. Rev. Lett. 70, 2964 (1993)PRLTAO0031-900710.1103/PhysRevLett.70.2964; Phys. Rev. E 53, 2670 (1996)1063-651X10.1103/PhysRevE.53.2670], and then we use the shape equation and linking conditions to prove that this conjecture holds not only for axisymmetric budding vesicles, but also for asymmetric ones. Our study reveals that the mean curvature at any point on the membrane segments adjacent to the neck satisfies the general neck condition for the limit shape of a budding vesicle when the length scale of the membrane segments is much larger than the characteristic size of the neck but still much smaller than the characteristic size of the vesicle.

Emerging Mechanisms and Roles for Asymmetric Cytokinesis

Cytokinesis completes cell division by physically separating the contents of the mother cell between the two daughter cells. This event requires the highly coordinated reorganization of the cytoskeleton within a precise window of time to ensure faithful genomic segregation. In addition, recent progress in the field highlighted the importance of cytokinesis in providing particularly important cues in the context of multicellular tissues. The organization of the cytokinetic machinery and the asymmetric localization or inheritance of the midbody remnants is critical to define the spatial distribution of mechanical and biochemical signals. After a brief overview of the conserved steps of animal cytokinesis, we review the mechanisms controlling polarized cytokinesis focusing on the challenges of epithelial cytokinesis. Finally, we discuss the significance of these asymmetries in defining embryonic body axes, determining cell fate, and ensuring the correct propagation of epithelial organization during proliferation.