Furrow constriction in animal cell cytokinesis

Mechanical power is maximized during contractile ring-like formation in a biomimetic dividing cell model

The spatial and temporal dynamics of forces in cells coordinate essential behaviors like division, polarization, and migration. While intracellular signaling initiates contractile ring assembly during cell division, how mechanical forces coordinate division and their energetic costs remain unclear. Here, we develop an in vitro model where myosin-induced stress drives division-like shape changes in giant unilamellar vesicles (GUVs, liposomes). Myosin activity is controlled by light patterns globally or locally at the equator. Global activation causes slow, shallow cleavage furrows due to a tug-of-war between the equatorial and polar forces. By contrast, local activation leads to faster, deeper, and symmetric division as equatorial forces dominate. Dissociating the actin cortex at the poles is crucial for inducing significant furrowing. During furrowing, actomyosin flows align actin filaments parallel to the division plane, forming a contractile ring-like structure. Mechanical power is not greatest during contraction, but is maximized just before furrowing. This study reveals the quantitative relationship between force patterning and mechanical energy during division-like shape changes, providing insights into cell division mechanics.

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.

A cytokinetic ring-driven cell rotation achieves Hertwig's rule in early development

Hertwig's rule states that cells divide along their longest axis, usually driven by forces acting on the mitotic spindle. Here, we show that in contrast to this rule, microtubule-based pulling forces in early Caenorhabditis elegans embryos align the spindle with the short axis of the cell. We combine theory with experiments to reveal that in order to correct this misalignment, inward forces generated by the constricting cytokinetic ring rotate the entire cell until the spindle is aligned with the cell's long axis. Experiments with slightly compressed mouse zygotes indicate that this cytokinetic ring-driven mechanism of ensuring Hertwig's rule is general for cells capable of rotating inside a confining shell, a scenario that applies to early cell divisions of many systems.

Aberrant cortex contractions impact mammalian oocyte quality

The cortex controls cell shape. In mouse oocytes, the cortex thickens in an Arp2/3-complex-dependent manner, ensuring chromosome positioning and segregation. Surprisingly, we identify that mouse oocytes lacking the Arp2/3 complex undergo cortical actin remodeling upon division, followed by cortical contractions that are unprecedented in mammalian oocytes. Using genetics, imaging, and machine learning, we show that these contractions stir the cytoplasm, resulting in impaired organelle organization and activity. Oocyte capacity to avoid polyspermy is impacted, leading to a reduced female fertility. We could diminish contractions and rescue cytoplasmic anomalies. Similar contractions were observed in human oocytes collected as byproducts during IVF (in vitro fertilization) procedures. These contractions correlate with increased cytoplasmic motion, but not with defects in spindle assembly or aneuploidy in mice or humans. Our study highlights a multiscale effect connecting cortical F-actin, contractions, and cytoplasmic organization and affecting oocyte quality, with implications for female fertility.

Odd elasticity and topological waves in active surfaces

Odd elasticity describes active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new antisymmetric (odd) components appear in the elastic tensor. In this work we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism. Unlike electronic Chern insulators where the magnetic field at the same time gaps the spectrum and imparts chirality, here the finite thickness of the sample gaps the shear modes, and the odd elasticity makes them chiral.

Learning a conserved mechanism for early neuroectoderm morphogenesis

Morphogenesis is the process whereby the body of an organism develops its target shape. The morphogen BMP is known to play a conserved role across bilaterian organisms in determining the dorsoventral (DV) axis. Yet, how BMP governs the spatio-temporal dynamics of cytoskeletal proteins driving morphogenetic flow remains an open question. Here, we use machine learning to mine a morphodynamic atlas of Drosophila development, and construct a mathematical model capable of predicting the coupled dynamics of myosin, E-cadherin, and morphogenetic flow. Mutant analysis shows that BMP sets the initial condition of this dynamical system according to the following signaling cascade: BMP establishes DV pair-rule-gene patterns that set-up an E-cadherin gradient which in turn creates a myosin gradient in the opposite direction through mechanochemical feedbacks. Using neural tube organoids, we argue that BMP, and the signaling cascade it triggers, prime the conserved dynamics of neuroectoderm morphogenesis from fly to humans.

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 .

Embryo mechanics cartography: inference of 3D force atlases from fluorescence microscopy

Tissue morphogenesis results from a tight interplay between gene expression, biochemical signaling and mechanics. Although sequencing methods allow the generation of cell-resolved spatiotemporal maps of gene expression, creating similar maps of cell mechanics in three-dimensional (3D) developing tissues has remained a real challenge. Exploiting the foam-like arrangement of cells, we propose a robust end-to-end computational method called 'foambryo' to infer spatiotemporal atlases of cellular forces from fluorescence microscopy images of cell membranes. Our method generates precise 3D meshes of cells' geometry and successively predicts relative cell surface tensions and pressures. We validate it with 3D foam simulations, study its noise sensitivity and prove its biological relevance in mouse, ascidian and worm embryos. 3D force inference allows us to recover mechanical features identified previously, but also predicts new ones, unveiling potential new insights on the spatiotemporal regulation of cell mechanics in developing embryos. Our code is freely available and paves the way for unraveling the unknown mechanochemical feedbacks that control embryo and tissue morphogenesis.

Shape transitions in a network model of active elastic shells

Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex 3D shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.

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.

Constriction of Actin Rings by Passive Crosslinkers

In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared with those of crosslinker-mediated microtubule sliding.

Modelling contractile ring formation and division to daughter cells for simulating proliferative multicellular dynamics

Cell proliferation is a fundamental process underlying embryogenesis, homeostasis, wound healing, and cancer. The process involves multiple events during each cell cycle, such as cell growth, contractile ring formation, and division to daughter cells, which affect the surrounding cell population geometrically and mechanically. However, existing methods do not comprehensively describe the dynamics of multicellular structures involving cell proliferation at a subcellular resolution. In this study, we present a novel model for proliferative multicellular dynamics at the subcellular level by building upon the nonconservative fluid membrane (NCF) model that we developed in earlier research. The NCF model utilizes a dynamically-rearranging closed triangular mesh to depict the shape of each cell, enabling us to analyze cell dynamics over extended periods beyond each cell cycle, during which cell surface components undergo dynamic turnover. The proposed model represents the process of cell proliferation by incorporating cell volume growth and contractile ring formation through an energy function and topologically dividing each cell at the cleavage furrow formed by the ring. Numerical simulations demonstrated that the model recapitulated the process of cell proliferation at subcellular resolution, including cell volume growth, cleavage furrow formation, and division to daughter cells. Further analyses suggested that the orientation of actomyosin stress in the contractile ring plays a crucial role in the cleavage furrow formation, i.e., circumferential orientation can form a cleavage furrow but isotropic orientation cannot. Furthermore, the model replicated tissue-scale multicellular dynamics, where the successive proliferation of adhesive cells led to the formation of a cell sheet and stratification on the substrate. Overall, the proposed model provides a basis for analyzing proliferative multicellular dynamics at subcellular resolution.

Cell protrusions and contractions generate long-range membrane tension propagation

Membrane tension is thought to be a long-range integrator of cell physiology. Membrane tension has been proposed to enable cell polarity during migration through front-back coordination and long-range protrusion competition. These roles necessitate effective tension transmission across the cell. However, conflicting observations have left the field divided as to whether cell membranes support or resist tension propagation. This discrepancy likely originates from the use of exogenous forces that may not accurately mimic endogenous forces. We overcome this complication by leveraging optogenetics to directly control localized actin-based protrusions or actomyosin contractions while simultaneously monitoring the propagation of membrane tension using dual-trap optical tweezers. Surprisingly, actin-driven protrusions and actomyosin contractions both elicit rapid global membrane tension propagation, whereas forces applied to cell membranes alone do not. We present a simple unifying mechanical model in which mechanical forces that engage the actin cortex drive rapid, robust membrane tension propagation through long-range membrane flows.

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.

Polarized branched Actin modulates cortical mechanics to produce unequal-size daughters during asymmetric division

The control of cell shape during cytokinesis requires a precise regulation of mechanical properties of the cell cortex. Only few studies have addressed the mechanisms underlying the robust production of unequal-sized daughters during asymmetric cell division. Here we report that unequal daughter-cell sizes resulting from asymmetric sensory organ precursor divisions in Drosophila are controlled by the relative amount of cortical branched Actin between the two cell poles. We demonstrate this by mistargeting the machinery for branched Actin dynamics using nanobodies and optogenetics. We can thereby engineer the cell shape with temporal precision and thus the daughter-cell size at different stages of cytokinesis. Most strikingly, inverting cortical Actin asymmetry causes an inversion of daughter-cell sizes. Our findings uncover the physical mechanism by which the sensory organ precursor mother cell controls relative daughter-cell size: polarized cortical Actin modulates the cortical bending rigidity to set the cell surface curvature, stabilize the division and ultimately lead to unequal daughter-cell size.

Active morphogenesis of patterned epithelial shells

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.

Interacting active surfaces: A model for three-dimensional cell aggregates

We introduce a modelling and simulation framework for cell aggregates in three dimensions based on interacting active surfaces. Cell mechanics is captured by a physical description of the acto-myosin cortex that includes cortical flows, viscous forces, active tensions, and bending moments. Cells interact with each other via short-range forces capturing the effect of adhesion molecules. We discretise the model equations using a finite element method, and provide a parallel implementation in C++. We discuss examples of application of this framework to small and medium-sized aggregates: we consider the shape and dynamics of a cell doublet, a planar cell sheet, and a growing cell aggregate. This framework opens the door to the systematic exploration of the cell to tissue-scale mechanics of cell aggregates, which plays a key role in the morphogenesis of embryos and organoids.

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.

Network model of active elastic shells swollen by hydrostatic pressure

Many organisms have an elastic skeleton that consists of a closed shell of epithelial cells that is filled with fluid, and can actively regulate both elastic forces in the shell and hydrostatic pressure inside it. In this work we introduce a simple network model of such pressure-stabilized active elastic shells in which cross-links are represented by material points connected by non-linear springs of some given equilibrium lengths and spring constants. We mimic active contractile forces in the system by changing the parameters of randomly chosen springs and use computer simulations to study the resulting local and global deformation dynamics of the network. We elucidate the statistical properties of these deformations by computing the corresponding distributions and correlation functions. We show that pressure-induced stretching of the network introduces coupling between its local and global behavior: while the network opposes the contraction of each excited spring and affects the amplitude and relaxation time of its deformation, random local excitations give rise to contraction of the network and to fluctuations of its surface area.

Actomyosin-Driven Division of a Synthetic Cell

One of the major challenges of bottom-up synthetic biology is rebuilding a minimal cell division machinery. From a reconstitution perspective, the animal cell division apparatus is mechanically the simplest and therefore attractive to rebuild. An actin-based ring produces contractile force to constrict the membrane. By contrast, microbes and plant cells have a cell wall, so division requires concerted membrane constriction and cell wall synthesis. Furthermore, reconstitution of the actin division machinery helps in understanding the physical and molecular mechanisms of cytokinesis in animal cells and thus our own cells. In this review, we describe the state-of-the-art research on reconstitution of minimal actin-mediated cytokinetic machineries. Based on the conceptual requirements that we obtained from the physics of the shape changes involved in cell division, we propose two major routes for building a minimal actin apparatus capable of division. Importantly, we acknowledge both the passive and active roles that the confining lipid membrane can play in synthetic cytokinesis. We conclude this review by identifying the most pressing challenges for future reconstitution work, thereby laying out a roadmap for building a synthetic cell equipped with a minimal actin division machinery.

Mechanics of stabilized intercellular bridges

Numerous engineered and natural systems form through reinforcement and stabilization of a deformed configuration that was generated by a transient force. An important class of such structures arises during gametogenesis, when a dividing cell undergoes incomplete cytokinesis, giving rise to daughter cells that remain connected through a stabilized intercellular bridge (ICB). ICBs can form through arrest of the contractile cytokinetic furrow and its subsequent stabilization. Despite knowledge of the molecular components, the mechanics underlying robust ICB assembly and the interplay between ring contractility and stiffening are poorly understood. Here, we report joint experimental and theoretical work that explores the physics underlying robust ICB assembly. We develop a continuum mechanics model that reveals the minimal requirements for the formation of stable ICBs, and validate the model's equilibrium predictions through a tabletop experimental analog. With insight into the equilibrium states, we turn to the dynamics: we demonstrate that contractility and stiffening are in dynamic competition and that the time intervals of their action must overlap to ensure assembly of ICBs of biologically observed proportions. Our results highlight a mechanism in which deformation and remodeling are tightly coordinated-one that is applicable to several mechanics-based applications and is a common theme in biological systems spanning several length scales.

Membrane area gain and loss during cytokinesis

In cytokinesis of animal cells, the cell is symmetrically divided into two. Since the cell's volume is conserved, the projected area has to increase to allow for the change of shape. Here we aim to predict how membrane gain and loss adapt during cytokinesis. We work with a kinetic model in which membrane turnover depends on membrane tension and cell shape. We apply this model to a series of calculated vesicle shapes as a proxy for the shape of dividing cells. We find that the ratio of kinetic turnover parameters changes nonmonotonically with cell shape, determined by the dependence of exocytosis and endocytosis on membrane curvature. Our results imply that controlling membrane turnover will be crucial for the successful division of artificial cells.

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.

Physical mechanisms of ESCRT-III-driven cell division

Living systems propagate by undergoing rounds of cell growth and division. Cell division is at heart a physical process that requires mechanical forces, usually exerted by assemblies of cytoskeletal polymers. Here we developed a physical model for the ESCRT-III-mediated division of archaeal cells, which despite their structural simplicity share machinery and evolutionary origins with eukaryotes. By comparing the dynamics of simulations with data collected from live cell imaging experiments, we propose that this branch of life uses a previously unidentified division mechanism. Active changes in the curvature of elastic cytoskeletal filaments can lead to filament perversions and supercoiling, to drive ring constriction and deform the overlying membrane. Abscission is then completed following filament disassembly. The model was also used to explore how different adenosine triphosphate (ATP)-driven processes that govern the way the structure of the filament is changed likely impact the robustness and symmetry of the resulting division. Comparisons between midcell constriction dynamics in simulations and experiments reveal a good agreement with the process when changes in curvature are implemented at random positions along the filament, supporting this as a possible mechanism of ESCRT-III-dependent division in this system. Beyond archaea, this study pinpoints a general mechanism of cytokinesis based on dynamic coupling between a coiling filament and the membrane.

Extracellular hyaluronate pressure shaped by cellular tethers drives tissue morphogenesis

How tissues acquire complex shapes is a fundamental question in biology and regenerative medicine. Zebrafish semicircular canals form from invaginations in the otic epithelium (buds) that extend and fuse to form the hubs of each canal. We find that conventional actomyosin-driven behaviors are not required. Instead, local secretion of hyaluronan, made by the enzymes uridine 5'-diphosphate dehydrogenase (ugdh) and hyaluronan synthase 3 (has3), drives canal morphogenesis. Charged hyaluronate polymers osmotically swell with water and generate isotropic extracellular pressure to deform the overlying epithelium into buds. The mechanical anisotropy needed to shape buds into tubes is conferred by a polarized distribution of actomyosin and E-cadherin-rich membrane tethers, which we term cytocinches. Most work on tissue morphogenesis ascribes actomyosin contractility as the driving force, while the extracellular matrix shapes tissues through differential stiffness. Our work inverts this expectation. Hyaluronate pressure shaped by anisotropic tissue stiffness may be a widespread mechanism for powering morphological change in organogenesis and tissue engineering.

Optogenetic relaxation of actomyosin contractility uncovers mechanistic roles of cortical tension during cytokinesis

Actomyosin contractility generated cooperatively by nonmuscle myosin II and actin filaments plays essential roles in a wide range of biological processes, such as cell motility, cytokinesis, and tissue morphogenesis. However, subcellular dynamics of actomyosin contractility underlying such processes remains elusive. Here, we demonstrate an optogenetic method to induce relaxation of actomyosin contractility at the subcellular level. The system, named OptoMYPT, combines a protein phosphatase 1c (PP1c)-binding domain of MYPT1 with an optogenetic dimerizer, so that it allows light-dependent recruitment of endogenous PP1c to the plasma membrane. Blue-light illumination is sufficient to induce dephosphorylation of myosin regulatory light chains and a decrease in actomyosin contractile force in mammalian cells and Xenopus embryos. The OptoMYPT system is further employed to understand the mechanics of actomyosin-based cortical tension and contractile ring tension during cytokinesis. We find that the relaxation of cortical tension at both poles by OptoMYPT accelerated the furrow ingression rate, revealing that the cortical tension substantially antagonizes constriction of the cleavage furrow. Based on these results, the OptoMYPT system provides opportunities to understand cellular and tissue mechanics.

Aurora B-dependent polarization of the cortical actomyosin network during mitotic exit

The isotropic metaphase actin cortex progressively polarizes as the anaphase spindle elongates during mitotic exit. This involves the loss of actomyosin cortex from opposing cell poles and the accumulation of an actomyosin belt at the cell centre. Although these spatially distinct cortical remodelling events are coordinated in time, here we show that they are independent of each other. Thus, actomyosin is lost from opposing poles in anaphase cells that lack an actomyosin ring owing to centralspindlin depletion. In examining potential regulators of this process, we identify a role for Aurora B kinase in actin clearance at cell poles. Upon combining Aurora B inhibition with centralspindlin depletion, cells exiting mitosis fail to change shape and remain completely spherical. Additionally, we demonstrate a requirement for Aurora B in the clearance of cortical actin close to anaphase chromatin in cells exiting mitosis with a bipolar spindle and in monopolar cells forced to divide while flat. Altogether, these data suggest a novel role for Aurora B activity in facilitating DNA-mediated polar relaxation at anaphase, polarization of the actomyosin cortex, and cell division.

A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics

We present a user-friendly and intuitive C++ expression system to implement numerical simulations of continuum biological hydrodynamics. The expression system allows writing simulation programs in near-mathematical notation and makes codes more readable, more compact, and less error-prone. It also cleanly separates the implementation of the partial differential equation model from the implementation of the numerical methods used to discretize it. This allows changing either of them with minimal changes to the source code. The presented expression system is implemented in the high-performance computing platform OpenFPM, supporting simulations that transparently parallelize on multi-processor computer systems. We demonstrate that our expression system makes it easier to write scalable codes for simulating biological hydrodynamics in space and time. We showcase the present framework in numerical simulations of active polar fluids, as well as in classic simulations of fluid dynamics from the incompressible Navier-Stokes equations to Stokes flow in a ball. The presented expression system accelerates scalable simulations of spatio-temporal models that encode the physics and material properties of tissues in order to algorithmically study morphogenesis.

Mitochondrial cristae modeled as an out-of-equilibrium membrane driven by a proton field

As the places where most of the fuel of the cell, namely, ATP, is synthesized, mitochondria are crucial organelles in eukaryotic cells. The shape of the invaginations of the mitochondria inner membrane, known as a crista, has been identified as a signature of the energetic state of the organelle. However, the interplay between the rate of ATP synthesis and the crista shape remains unclear. In this work, we investigate the crista membrane deformations using a pH-dependent Helfrich model, maintained out of equilibrium by a diffusive flux of protons. This model gives rise to shape changes of a cylindrical invagination, in particular to the formation of necks between wider zones under variable, and especially oscillating, proton flux.

Contractile ring constriction and septation in fission yeast are integrated mutually stabilizing processes.. [DOI: 10.1101/2021.06.25.449700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In common with other cellular machineries, the actomyosin contractile ring that divides cells during cytokinesis does not operate in isolation. Contractile rings in animal cells interact with contiguous actomyosin cortex, while ring constriction in many cell-walled organisms couples tightly to cell wall growth. In fission yeast, a septum grows in the wake of the constricting ring, ensuring cytokinesis leaves two daughter cells fully enclosed by cell wall. Here we mathematical modeled the integrated constriction-septation system in fission yeast, with a kinetic growth model evolving the 3D septum shape coupled to a molecularly explicit simulation of the contractile ring highly constrained by experimental data. Simulations revealed influences in both directions, stabilizing the ring-septum system as a whole. By providing a smooth circular anchoring surface for the ring, the inner septum leading edge stabilized ring organization and tension production; by mechanically regulating septum circularity and in-plane growth, ring tension stabilized septum growth and shape. Genetic or pharmacological perturbation of either subsystem destabilized this delicate balance, precipitating uncontrolled positive feedback with disastrous morphological and functional consequences. Thus, high curvature septum irregularities triggered bridging instabilities, in which contractile ring segments became unanchored. Bridging abolished the local tension-mediated septum shape regulation, exacerbating the irregularity in a mutually destabilizing runaway process. Our model explains a number of previously mysterious experimental observations, including unanchoring of ring segments observed in cells with mutations in the septum-growing β-glucan synthases, and irregular septa in cells with mutations in the contractile ring myosin-II Myo2. Thus, the contractile ring and cell wall growth cellular machineries operate as a single integrated system, whose stability relies on mutual regulation by the two subsystems.

The dual functions of Rab11 and Rab35 GTPases-regulation of cell division and promotion of tumorigenicity

The broad studies of cancer have led researchers to the creditable understanding of biological and environmental factors that make benign cells to become malignant, as well as the developmental aspects of the tumour cells, known as the "hallmarks of cancer". However, additional research is needed to uncover the features of cancer biology, which would allow to design new and more effective treatment strategies for cancer patients. Since RabGTPases and their effectors are frequently altered in cancer, their role in a regulation of cell division leading to the acquisition of cancer cell-like phenotype has drawn a lot of attention from different research groups in recent years. Both, Rab11 and Rab35 belong to a superfamily of small monomeric GTPases that regulate a diverse array of cellular functions. Lately, Rab11 and Rab35 were declared as oncogenic, and because of their association with abundant cellular functions, a linkage to the induction of cancer, has been proposed. Although the clear connection between the improper regulation of Rab11 or Rab35 and the initiation of tumorigenicity has only beginning to emerge, in this review we will discuss the newest findings regarding the participation of RabGTPases in a control of cell division and promotion of tumorigenesis, trying to link the actual function to the cancer causality.

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.

Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.

Polar relaxation by dynein-mediated removal of cortical myosin II

Nearly six decades ago, Lewis Wolpert proposed the relaxation of the polar cell cortex by the radial arrays of astral microtubules as a mechanism for cleavage furrow induction. While this mechanism has remained controversial, recent work has provided evidence for polar relaxation by astral microtubules, although its molecular mechanisms remain elusive. Here, using C. elegans embryos, we show that polar relaxation is achieved through dynein-mediated removal of myosin II from the polar cortexes. Mutants that position centrosomes closer to the polar cortex accelerated furrow induction, whereas suppression of dynein activity delayed furrowing. We show that dynein-mediated removal of myosin II from the polar cortexes triggers a bidirectional cortical flow toward the cell equator, which induces the assembly of the actomyosin contractile ring. These results provide a molecular mechanism for the aster-dependent polar relaxation, which works in parallel with equatorial stimulation to promote robust cytokinesis.

Extracellular matrix in multicellular aggregates acts as a pressure sensor controlling cell proliferation and motility

Imposed deformations play an important role in morphogenesis and tissue homeostasis, both in normal and pathological conditions. To perceive mechanical perturbations of different types and magnitudes, tissues need appropriate detectors, with a compliance that matches the perturbation amplitude. By comparing results of selective osmotic compressions of CT26 mouse cells within multicellular aggregates and global aggregate compressions, we show that global compressions have a strong impact on the aggregates growth and internal cell motility, while selective compressions of same magnitude have almost no effect. Both compressions alter the volume of individual cells in the same way over a shor-timescale, but, by draining the water out of the extracellular matrix, the global one imposes a residual compressive mechanical stress on the cells over a long-timescale, while the selective one does not. We conclude that the extracellular matrix is as a sensor that mechanically regulates cell proliferation and migration in a 3D environment.

Cell Junction Mechanics beyond the Bounds of Adhesion and Tension

Cell-cell junctions, in particular adherens junctions, are major determinants of tissue mechanics during morphogenesis and homeostasis. In attempts to link junctional mechanics to tissue mechanics, many have utilized explicitly or implicitly equilibrium approaches based on adhesion energy, surface energy, and contractility to determine the mechanical equilibrium at junctions. However, it is increasingly clear that they have significant limitations, such as that it remains challenging to link the dynamics of the molecular components to the resulting physical properties of the junction, to its remodeling ability, and to its adhesion strength. In this perspective, we discuss recent attempts to consider the aspect of energy dissipation at junctions to draw contact points with soft matter physics where energy loss plays a critical role in adhesion theories. We set the grounds for a theoretical framework of the junction mechanics that bridges the dynamics at the molecular scale to the mechanics at the tissue scale.

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'.

Equatorial Non-muscle Myosin II and Plastin Cooperate to Align and Compact F-actin Bundles in the Cytokinetic Ring

Cytokinesis is the last step of cell division that physically partitions the mother cell into two daughter cells. Cytokinesis requires the assembly and constriction of a contractile ring, a circumferential array of filamentous actin (F-actin), non-muscle myosin II motors (myosin), and actin-binding proteins that forms at the cell equator. Cytokinesis is accompanied by long-range cortical flows from regions of relaxation toward regions of compression. In the C. elegans one-cell embryo, it has been suggested that anterior-directed cortical flows are the main driver of contractile ring assembly. Here, we use embryos co-expressing motor-dead and wild-type myosin to show that cortical flows can be severely reduced without major effects on contractile ring assembly and timely completion of cytokinesis. Fluorescence recovery after photobleaching in the ingressing furrow reveals that myosin recruitment kinetics are also unaffected by the absence of cortical flows. We find that myosin cooperates with the F-actin crosslinker plastin to align and compact F-actin bundles at the cell equator, and that this cross-talk is essential for cytokinesis. Our results thus argue against the idea that cortical flows are a major determinant of contractile ring assembly. Instead, we propose that contractile ring assembly requires localized concerted action of motor-competent myosin and plastin at the cell equator.

Tug-of-war between stretching and bending in living cell sheets

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness e of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like 1/e, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

Flow-accelerated platelet biogenesis is due to an elasto-hydrodynamic instability

Blood platelets are formed by fragmentation of long membrane extensions from bone marrow megakaryocytes in the blood flow. Using lattice-Boltzmann/immersed boundary simulations we propose a biological Rayleigh-Plateau instability as the biophysical mechanism behind this fragmentation process. This instability is akin to the surface tension-induced breakup of a liquid jet but is driven by active cortical processes including actomyosin contractility and microtubule sliding. Our fully three-dimensional simulations highlight the crucial role of actomyosin contractility, which is required to trigger the instability, and illustrate how the wavelength of the instability determines the size of the final platelets. The elasto-hydrodynamic origin of the fragmentation explains the strong acceleration of platelet biogenesis in the presence of an external flow, which we observe in agreement with experiments. Our simulations then allow us to disentangle the influence of specific flow conditions: While a homogeneous flow with uniform velocity leads to the strongest acceleration, a shear flow with a linear velocity gradient can cause fusion events of two developing platelet-sized swellings during fragmentation. A fusion event may lead to the release of larger structures which are observable as preplatelets in experiments. Together, our findings strongly indicate a mainly physical origin of fragmentation and regulation of platelet size in flow-accelerated platelet biogenesis.

Ends and middle: Global force balance and septum location in fission yeast

The fission yeast cell is shaped as a very regular cylinder ending by hemi-spheres at both cell ends. Its conserved phenotypes are often used as read-outs for classifying interacting genes and protein networks. Using Pascal and Young-Laplace laws, we proposed a framework where scaling arguments predicted shapes. Here we probed quantitatively one of these relations which predicts that the division site would be located closer to the cell end with the larger radius of curvature. By combining genetics and quantitative imaging, we tested experimentally whether altered shapes of cell end correlate with a displaced division site, leading to asymmetric cell division. Our results show that the division site position depends on the radii of curvatures of both ends. This new geometrical mechanism for the proper division plane positioning could be essential to achieve even partitioning of cellular material at each cell division.

A quantitative high-resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. This paper considers as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells' response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important.

Mechanical stress induces a scalable switch in cortical flow polarization during cytokinesis

During animal development, cells need to sense and adapt to mechanical forces from their environment. Ultimately, these forces are transduced through the actomyosin cortex. How the cortex simultaneously responds to and creates forces during cytokinesis is not well understood. Here we show that, under mechanical stress, cortical actomyosin flow can switch polarization during cytokinesis in the C. elegans embryo. In unstressed embryos, longitudinal cortical flow contributes to contractile ring formation, while rotational cortical flow is additionally induced in uniaxially loaded embryos, i.e. embryos compressed between two plates. Rotational flow depends on astral microtubule signals and is required for the redistribution of the actomyosin cortex in loaded embryos. Rupture of longitudinally aligned cortical fibers during cortex rotation releases tension, initiates orthogonal longitudinal flow and, thereby, contributes to furrowing in loaded embryos. Moreover, actomyosin regulators involved in RhoA regulation, cortical polarity and chirality are all required for rotational flow, and become essential for cytokinesis under mechanical stress. In sum, our findings extend the current framework of mechanical stress response during cell division and show scaling of orthogonal cortical flows to the amount of mechanical stress.

Crawling in a Fluid

There is increasing evidence that mammalian cells not only crawl on substrates but can also swim in fluids. To elucidate the mechanisms of the onset of motility of cells in suspension, a model which couples actin and myosin kinetics to fluid flow is proposed and solved for a spherical shape. The swimming speed is extracted in terms of key parameters. We analytically find super- and subcritical bifurcations from a nonmotile to a motile state and also spontaneous polarity oscillations that arise from a Hopf bifurcation. Relaxing the spherical assumption, the obtained shapes show appealing trends.

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.