Relaxation and Noise-Driven Oscillations in a Model of Mitotic Spindle Dynamics.

During cell division, the mitotic spindle moves dynamically through the cell to position the chromosomes and determine the ultimate spatial position of the two daughter cells. These movements have been attributed to the action of cortical force generators which pull on the astral microtubules to position the spindle, as well as pushing events by these same microtubules against the cell cortex and plasma membrane. Attachment and detachment of cortical force generators working antagonistically against centring forces of microtubules have been modelled previously (Grill et al. in Phys Rev Lett 94:108104, 2005) via stochastic simulations and mean-field Fokker-Planck equations (describing random motion of force generators) to predict oscillations of a spindle pole in one spatial dimension. Using systematic asymptotic methods, we reduce the Fokker-Planck system to a set of ordinary differential equations (ODEs), consistent with a set proposed by Grill et al., which can provide accurate predictions of the conditions for the Fokker-Planck system to exhibit oscillations. In the limit of small restoring forces, we derive an algebraic prediction of the amplitude of spindle-pole oscillations and demonstrate the relaxation structure of nonlinear oscillations. We also show how noise-induced oscillations can arise in stochastic simulations for conditions in which the mean-field Fokker-Planck system predicts stability, but for which the period can be estimated directly by the ODE model and the amplitude by a related stochastic differential equation that incorporates random binding kinetics.

Meeting report - Dynamic Cell III.

Dynamic Cell III, a meeting jointly organized by the British Society of Cell Biology (BSCB) and the Biochemical Society, took place at the Manchester Conference Centre, Manchester, UK in March 2018. It brought together a diverse group of scientists from around the world, all with a shared interest in understanding how dynamic functions of the cell are fulfilled. A particular focus was the regulation of the cytoskeleton: in cell division, cell migration and cell-cell interactions. Moreover, a key theme that ran through all presented work was the development of new and exciting technologies to study dynamic cell behaviour.

Xenopus as a model for studies in mechanical stress and cell division.

We exist in a physical world, and cells within biological tissues must respond appropriately to both environmental forces and forces generated within the tissue to ensure normal development and homeostasis. Cell division is required for normal tissue growth and maintenance, but both the direction and rate of cell division must be tightly controlled to avoid diseases of over-proliferation such as cancer. Recent studies have shown that mechanical cues can cause mitotic entry and orient the mitotic spindle, suggesting that physical force could play a role in patterning tissue growth. However, to fully understand how mechanics guides cells in vivo, it is necessary to assess the interaction of mechanical strain and cell division in a whole tissue context. In this mini-review we first summarise the body of work linking mechanics and cell division, before looking at the advantages that the Xenopus embryo can offer as a model organism for understanding: (1) the mechanical environment during embryogenesis, and (2) factors important for cell division. Finally, we introduce a novel method for applying a reproducible strain to Xenopus embryonic tissue and assessing subsequent cell divisions.

Force and the spindle: mechanical cues in mitotic spindle orientation.

The mechanical environment of a cell has a profound effect on its behaviour, from dictating cell shape to driving the transcription of specific genes. Recent studies have demonstrated that mechanical forces play a key role in orienting the mitotic spindle, and therefore cell division, in both single cells and tissues. Whilst the molecular machinery that mediates the link between external force and the mitotic spindle remains largely unknown, it is becoming increasingly clear that this is a widely used mechanism which could prove vital for coordinating cell division orientation across tissues in a variety of contexts.

ERK and phosphoinositide 3-kinase temporally coordinate different modes of actin-based motility during embryonic wound healing.

Embryonic wound healing provides a perfect example of efficient recovery of tissue integrity and homeostasis, which is vital for survival. Tissue movement in embryonic wound healing requires two functionally distinct actin structures: a contractile actomyosin cable and actin protrusions at the leading edge. Here, we report that the discrete formation and function of these two structures is achieved by the temporal segregation of two intracellular upstream signals and distinct downstream targets. The sequential activation of ERK and phosphoinositide 3-kinase (PI3K) signalling divides Xenopus embryonic wound healing into two phases. In the first phase, activated ERK suppresses PI3K activity, and is responsible for the activation of Rho and myosin-2, which drives actomyosin cable formation and constriction. The second phase is dominated by restored PI3K signalling, which enhances Rac and Cdc42 activity, leading to the formation of actin protrusions that drive migration and zippering. These findings reveal a new mechanism for coordinating different modes of actin-based motility in a complex tissue setting, namely embryonic wound healing.

Sculpting an Embryo: The Interplay between Mechanical Force and Cell Division.

The journey from a single fertilised cell to a multicellular organism is, at the most fundamental level, orchestrated by mitotic cell divisions. Both the rate and the orientation of cell divisions are important in ensuring the proper development of an embryo. Simultaneous with cell proliferation, embryonic cells constantly experience a wide range of mechanical forces from their surrounding tissue environment. Cells must be able to read and respond correctly to these forces since they are known to affect a multitude of biological functions, including cell divisions. The interplay between the mechanical environment and cell divisions is particularly crucial during embryogenesis when tissues undergo dynamic changes in their shape, architecture, and overall organisation to generate functional tissues and organs. Here we review our current understanding of the cellular mechanisms by which mechanical force regulates cell division and place this knowledge within the context of embryogenesis and tissue morphogenesis.

Wound healing recapitulates morphogenesis in Drosophila embryos.

The capacity to repair a wound is a fundamental survival mechanism that is activated at any site of damage throughout embryonic and adult life. To study the cell biology and genetics of this process, we have developed a wounding model in Drosophila melanogaster embryos that allows live imaging of rearrangements and changes in cell shape, and of the cytoskeletal machinery that draws closed an in vivo wound. Using embryos expressing green fluorescent protein (GFP) fusion proteins, we show that two cytoskeletal-dependent elements -- an actin cable and dynamic filopodial/lamellipodial protrusions -- are expressed by epithelial cells at the wound edge and are pivotal for repair. Modulating the activities of the small GTPases Rho and Cdc42 demonstrates that these actin-dependent elements have differing cellular functions, but that either alone can drive wound closure. The actin cable operates as a 'purse-string' to draw the hole closed, whereas filopodia are essential for the final 'knitting' together of epithelial cells at the end of repair. Our data suggest a more complex model for epithelial repair than previously envisaged and highlight remarkable similarities with the well-characterized morphogenetic movement of dorsal closure in Drosophila.

Generation of anisotropic strain dysregulates wild-type cell division at the interface between host and oncogenic tissue.

Epithelial tissues are highly sensitive to anisotropies in mechanical force, with cells altering fundamental behaviors, such as cell adhesion, migration, and cell division.1-5 It is well known that, in the later stages of carcinoma (epithelial cancer), the presence of tumors alters the mechanical properties of a host tissue and that these changes contribute to disease progression.6-9 However, in the earliest stages of carcinoma, when a clonal cluster of oncogene-expressing cells first establishes in the epithelium, the extent to which mechanical changes alter cell behavior in the tissue as a whole remains unclear. This is despite knowledge that many common oncogenes, such as oncogenic Ras, alter cell stiffness and contractility.10-13 Here, we investigate how mechanical changes at the cellular level of an oncogenic cluster can translate into the generation of anisotropic strain across an epithelium, altering cell behavior in neighboring host tissue. We generated clusters of oncogene-expressing cells within otherwise normal in vivo epithelium, using Xenopus laevis embryos. We find that cells in kRasV12, but not cMYC, clusters have increased contractility, which introduces radial stress in the tissue and deforms surrounding host cells. The strain imposed by kRasV12 clusters leads to increased cell division and altered division orientation in neighboring host tissue, effects that can be rescued by reducing actomyosin contractility specifically in the kRasV12 cells. Our findings indicate that some oncogenes can alter the mechanical and proliferative properties of host tissue from the earliest stages of cancer development, changes that have the potential to contribute to tumorigenesis.

Morphogenesis: joining the dots to shape an embryo.

In the study of morphogenesis, how upstream signalling events are intricately linked to downstream cytoskeletal organisation is not entirely understood. Recent work in the Drosophila embryo has begun to shed light on this problem.

Don't Fence Me In: How Cancer Cells Divide in Crowded Spaces.

Cells in our body have to divide within a defined tissue space, which in tumors is more restricted than in normal tissue. In this issue of Developmental Cell, Matthews et al. (2020) reveal that oncogenic RasV12-mediated cell rounding and cortical stiffening promote cell division under confined conditions that are similar to those in tumors.

Applying Tensile and Compressive Force to Xenopus Animal Cap Tissue.

Over many years, the Xenopus laevis embryo has provided a powerful model system to investigate how mechanical forces regulate cellular function. Here, we describe a system to apply reproducible tensile and compressive force to X. laevis animal cap tissue explants and to simultaneously assess cellular behavior using live confocal imaging.

Force networks, torque balance and Airy stress in the planar vertex model of a confluent epithelium.

The vertex model is a popular framework for modelling tightly packed biological cells, such as confluent epithelia. Cells are described by convex polygons tiling the plane and their equilibrium is found by minimizing a global mechanical energy, with vertex locations treated as degrees of freedom. Drawing on analogies with granular materials, we describe the force network for a localized monolayer and derive the corresponding discrete Airy stress function, expressed for each N-sided cell as N scalars defined over kites covering the cell. We show how a torque balance (commonly overlooked in implementations of the vertex model) requires each internal vertex to lie at the orthocentre of the triangle formed by neighbouring edge centroids. Torque balance also places a geometric constraint on the stress in the neighbourhood of cellular trijunctions, and requires cell edges to be orthogonal to the links of a dual network that connect neighbouring cell centres and thereby triangulate the monolayer. We show how the Airy stress function depends on cell shape when a standard energy functional is adopted, and discuss implications for computational implementations of the model.

Dynamic analysis of dorsal closure in Drosophila: from genetics to cell biology.

Throughout development a series of epithelial bendings, sweepings, and fusions occur that collectively give shape to the embryo. These morphogenetic movements are driven by coordinated assembly and contraction of the actomyosin cytoskeleton in restricted populations of epithelial cells. One well-studied example of such a morphogenetic episode is dorsal closure in Drosophila embryogenesis. This process is tractable at a genetic level and has recently become the focus of live cell biology analysis because of the availability of flies expressing GFP-fusion proteins. This marriage of genetics and cell biology is very powerful and is allowing the dissection of fundamental signaling mechanisms that regulate the cytoskeletal reorganizations and contractions underlying coordinated tissue movements in the embryo.

Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis.

Distinct mechanisms involving cell shape and mechanical force are known to influence the rate and orientation of division in cultured cells. However, uncoupling the impact of shape and force in tissues remains challenging. Combining stretching of Xenopus tissue with mathematical methods of inferring relative mechanical stress, we find separate roles for cell shape and mechanical stress in orienting and cueing division. We demonstrate that division orientation is best predicted by an axis of cell shape defined by the position of tricellular junctions (TCJs), which align with local cell stress rather than tissue-level stress. The alignment of division to cell shape requires functional cadherin and the localization of the spindle orientation protein, LGN, to TCJs but is not sensitive to relative cell stress magnitude. In contrast, proliferation rate is more directly regulated by mechanical stress, being correlated with relative isotropic stress and decoupled from cell shape when myosin II is depleted.

Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model.

Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. The model predicts that mechanical interactions can generate mesoscopic patterns within the monolayer that exhibit long-range correlations in cell shape. The model also suggests that the orientation of mechanical and geometric cues for processes such as cell division are likely to be strongly correlated in real epithelia. Some limitations of the model in capturing geometric features of Xenopus epithelial cells are highlighted.

Mechanical characterization of disordered and anisotropic cellular monolayers.

We consider a cellular monolayer, described using a vertex-based model, for which cells form a spatially disordered array of convex polygons that tile the plane. Equilibrium cell configurations are assumed to minimize a global energy defined in terms of cell areas and perimeters; energy is dissipated via dynamic area and length changes, as well as cell neighbor exchanges. The model captures our observations of an epithelium from a Xenopus embryo showing that uniaxial stretching induces spatial ordering, with cells under net tension (compression) tending to align with (against) the direction of stretch, but with the stress remaining heterogeneous at the single-cell level. We use the vertex model to derive the linearized relation between tissue-level stress, strain, and strain rate about a deformed base state, which can be used to characterize the tissue's anisotropic mechanical properties; expressions for viscoelastic tissue moduli are given as direct sums over cells. When the base state is isotropic, the model predicts that tissue properties can be tuned to a regime with high elastic shear resistance but low resistance to area changes, or vice versa.

An interaction between myosin-10 and the cell cycle regulator Wee1 links spindle dynamics to mitotic progression in epithelia.

Anaphase in epithelia typically does not ensue until after spindles have achieved a characteristic position and orientation, but how or even if cells link spindle position to anaphase onset is unknown. Here, we show that myosin-10 (Myo10), a motor protein involved in epithelial spindle dynamics, binds to Wee1, a conserved regulator of cyclin-dependent kinase 1 (Cdk1). Wee1 inhibition accelerates progression through metaphase and disrupts normal spindle dynamics, whereas perturbing Myo10 function delays anaphase onset in a Wee1-dependent manner. Moreover, Myo10 perturbation increases Wee1-mediated inhibitory phosphorylation on Cdk1, which, unexpectedly, concentrates at cell-cell junctions. Based on these and other results, we propose a model in which the Myo10-Wee1 interaction coordinates attainment of spindle position and orientation with anaphase onset.

Dynamic analysis of actin cable function during Drosophila dorsal closure.

Throughout development, a series of epithelial movements and fusions occur that collectively shape the embryo. They are dependent on coordinated reorganizations and contractions of the actin cytoskeleton within defined populations of epithelial cells. One paradigm morphogenetic movement, dorsal closure in the Drosophila embryo, involves closure of a dorsal epithelial hole by sweeping of epithelium from the two sides of the embryo over the exposed extraembryonic amnioserosa to form a seam where the two epithelial edges fuse together. The front row cells exhibit a thick actin cable at their leading edge. Here, we test the function of this cable by live analysis of GFP-actin-expressing embryos in which the cable is disrupted by modulating Rho1 signaling or by loss of non-muscle myosin (Zipper) function. We show that the cable serves a dual role during dorsal closure. It is contractile and thus can operate as a "purse string," but it also restricts forward movement of the leading edge and excess activity of filopodia/lamellipodia. Stripes of epithelium in which cable assembly is disrupted gain a migrational advantage over their wild-type neighbors, suggesting that the cable acts to restrain front row cells, thus maintaining a taut, free edge for efficient zippering together of the epithelial sheets.

Dynein light intermediate chains maintain spindle bipolarity by functioning in centriole cohesion.

Cytoplasmic dynein 1 (dynein) is a minus end-directed microtubule motor protein with many cellular functions, including during cell division. The role of the light intermediate chains (LICs; DYNC1LI1 and 2) within the complex is poorly understood. In this paper, we have used small interfering RNAs or morpholino oligonucleotides to deplete the LICs in human cell lines and Xenopus laevis early embryos to dissect the LICs' role in cell division. We show that although dynein lacking LICs drives microtubule gliding at normal rates, the LICs are required for the formation and maintenance of a bipolar spindle. Multipolar spindles with poles that contain single centrioles were formed in cells lacking LICs, indicating that they are needed for maintaining centrosome integrity. The formation of multipolar spindles via centrosome splitting after LIC depletion could be rescued by inhibiting Eg5. This suggests a novel role for the dynein complex, counteracted by Eg5, in the maintenance of centriole cohesion during mitosis.