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.

Polarized interfacial tension induces collective migration of cells, as a cluster, in a 3D tissue.

In embryogenesis and cancer invasion, cells collectively migrate as a cluster in 3D tissues. Many studies have elucidated mechanisms of either individual or collective cell migration on 2D substrates; however, it remains unclear how cells collectively migrate as a cluster through 3D tissues. To address this issue, we considered the interfacial tension at cell-cell boundaries expressing cortical actomyosin contractions and cell-cell adhesive interactions. The strength of this tension is polarized; i.e., spatially biased within each cell according to a chemoattractant gradient. Using a 3D vertex model, we performed numerical simulations of multicellular dynamics in 3D space. The simulations revealed that the polarized interfacial tension enables cells to migrate collectively as a cluster through a 3D tissue. In this mechanism, interfacial tension induces unidirectional flow of each cell surface from the front to the rear along the cluster surface. Importantly, this mechanism does not necessarily require convection of cells, i.e., cell rearrangement, within the cluster. Moreover, several migratory modes were induced, depending on the strengths of polarity, adhesion, and noise; i.e., cells migrate either as single cells, as a cluster, or aligned like beads on a string, as occurs in embryogenesis and cancer invasion. These results indicate that the simple expansion and contraction of cell-cell boundaries enables cells to move directionally forward and to produce the variety of collective migratory movements observed in living systems.

Continuum modeling of non-conservative fluid membrane for simulating long-term cell dynamics.

Living cells actively deform and move by their force generations in three-dimensional (3D) space. These 3D cell dynamics occur over a long-term time scale, ranging from tens of minutes to days. On such a time scale, turnover of cell membrane constituents due to endocytosis and exocytosis cannot be ignored, i.e., the surface membrane dynamically deforms without mass conservation. Although membrane turnover is essential for large deformation of cells, there is no computational framework yet to simulate long-term cell dynamics with a non-conservative fluidic membrane. In this paper, we proposed a computational framework for simulating the long-term dynamics of a cell membrane in 3D space. For this purpose, in the proposed framework, the cell surface membrane is treated as a viscous fluid membrane without mass conservation. Cell shape is discretized by a triangular mesh, and its dynamics are expressed by effective energy and dissipation function. The mesh structure, distorted by membrane motion, is dynamically optimized by introducing a modified dynamic remeshing method. To validate the proposed framework, numerical simulations were performed, showing that the membrane flow is reproduced in a physically consistent manner and that the artificial effects of the remeshing method were negligible. To further demonstrate the applicability of the proposed framework, numerical simulations of cell migration induced by a mechanism similar to the Marangoni effect, i.e., the polarized surface tension actively generated by the cell, were performed. The observed cell behaviors agreed with existing analytical solutions, indicating that the proposed computational framework can quantitatively reproduce long-term active cell dynamics with membrane turnover. Based on the simple description of cell membrane dynamics, this framework provides a useful basis for analyzing various cell shaping and movement.

A Mechanical Instability in Planar Epithelial Monolayers Leads to Cell Extrusion.

In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal transition, or precancerous cell invasion. They play important roles in embryogenesis, homeostasis, carcinogenesis, and many other biological processes. Although many of the molecular factors involved in cell extrusion are known, little is known about the mechanical basis of cell extrusion. We used a three-dimensional (3D) vertex model to investigate the mechanical stability of cells arranged in a monolayer with 3D foam geometry. We found that when the cells composing the monolayer have homogeneous mechanical properties, cells are extruded from the monolayer when the symmetry of the 3D geometry is broken because of an increase in cell density or a decrease in the number of topological neighbors around single cells. Those results suggest that mechanical instability inherent in the 3D foam geometry of epithelial monolayers is sufficient to drive epithelial cell extrusion. In the situation in which cells in the monolayer actively generate contractile or adhesive forces under the control of intrinsic genetic programs, the forces act to break the symmetry of the monolayer, leading to cell extrusion that is directed to the apical or basal side of the monolayer by the balance of contractile and adhesive forces on the apical and basal sides. Although our analyses are based on a simple mechanical model, our results are in accordance with observations of epithelial monolayers in vivo and consistently explain cell extrusions under a wide range of physiological and pathophysiological conditions. Our results illustrate the importance of a mechanical understanding of cell extrusion and provide a basis by which to link molecular regulation to physical processes.

Apical Junctional Fluctuations Lead to Cell Flow while Maintaining Epithelial Integrity.

Epithelial sheet integrity is robustly maintained during morphogenesis, which is essential to shape organs and embryos. While maintaining the planar monolayer in three-dimensional space, cells dynamically flow via rearranging their connections between each other. However, little is known about how cells maintain the plane sheet integrity in three-dimensional space and provide cell flow in the in-plane sheet. In this study, using a three-dimensional vertex model, we demonstrate that apical junctional fluctuations allow stable cell rearrangements while ensuring monolayer integrity. In addition to the fluctuations, direction-dependent contraction on the apical cell boundaries, which corresponds to forces from adherens junctions, induces cell flow in a definite direction. We compared the kinematic behaviors of this apical-force-driven cell flow with those of typical cell flow that is driven by forces generated on basal regions and revealed the characteristic differences between them. These differences can be used to distinguish the mechanism of epithelial cell flow observed in experiments, i.e., whether it is apical- or basal-force-driven. Our numerical simulations suggest that cells actively generate fluctuations and use them to regulate both epithelial integrity and plasticity during morphogenesis.

Emergence of dorsal-ventral polarity in ESC-derived retinal tissue.

We previously demonstrated that mouse embryonic stem cell (mESC)-derived retinal epithelium self-forms an optic cup-like structure. In the developing retina, the dorsal and ventral sides differ in terms of local gene expression and morphological features. This aspect has not yet been shown in vitro Here, we demonstrate that mESC-derived retinal tissue spontaneously acquires polarity reminiscent of the dorsal-ventral (D-V) patterning of the embryonic retina. Tbx5 and Vax2 were expressed in a mutually exclusive manner, as seen in vivo Three-dimensional morphometric analysis showed that the in vitro-formed optic cup often contains cleft structures resembling the embryonic optic fissure. To elucidate the mechanisms underlying the spontaneous D-V polarization of mESC-derived retina, we examined the effects of patterning factors, and found that endogenous BMP signaling plays a predominant role in the dorsal specification. Further analysis revealed that canonical Wnt signaling, which was spontaneously activated at the proximal region, acts upstream of BMP signaling for dorsal specification. These observations suggest that D-V polarity could be established within the self-formed retinal neuroepithelium by intrinsic mechanisms involving the spatiotemporal regulation of canonical Wnt and BMP signals.

Topological graph description of multicellular dynamics based on vertex model.

Vertex models are generally powerful tools for exploring biological insights into multicellular dynamics. In these models, a multicellular structure is represented by a network, which is dynamically rearranged using topological operations. Remarkably, the topological dynamics of the network are important in guaranteeing the results from the models and their biological implications. However, it remains unclear whether the entire pattern of multicellular topological dynamics can be accurately expressed by a set of operators in the models. Surprisingly, vertex models have been empirically used for several decades without any mathematical verification. In this study, we propose a rigorous two-/three-dimensional (2D/3D) vertex model to describe multicellular topological dynamics. To do this, we classify several types of vertex models from a graph-theoretic perspective. Based on the classification, mathematical analyses reveal several conditions that enable us to apply the operators accurately without topological errors. Under these conditions, the operators can completely express the entire pattern of multicellular topological dynamics. From these results, we newly propose rigorous 2D/3D vertex models that can be applied to general multicellular dynamics, and we clarify several points to verify the results obtained from previous models.

Mechanical role of the spatial patterns of contractile cells in invagination of growing epithelial tissue.

Epithelial invagination is one of the fundamental deformation modes during morphogenesis, and is essential for deriving the three-dimensional shapes of organs from a flat epithelial sheet. Invagination occurs in an orderly manner according to the spatial pattern of the contractile cells; however, it remains elusive how tissue deformation can be caused by cellular activity in the patterned region. In this study, we investigated the mechanical role of the spatial patterns of the contractile cells in invagination of growing tissue using multicellular dynamics simulations. We found that cell proliferation and apical constriction were responsible for expanding the degree of tissue deformation and determining the location of the deformation, respectively. The direction of invagination depended on the spatial pattern of the contractile cells. Further, comparing the simulation results of surface and line contractions as possible modes of apical constriction, we found that the direction of invagination differed between these two modes even if the spatial pattern was the same. These results indicate that the buckling of the epithelial cell sheet caused by cell proliferation causes the invagination, with the direction and location determined by the configuration of the wedge-shaped cells given by the spatial pattern of the contractile cells.

Contractile actin belt and mesh structures provide the opposite dependence of epithelial stiffness on the spontaneous curvature of constituent cells.

Actomyosin generates contractile forces within cells, which have a crucial role in determining the macroscopic mechanical properties of epithelial tissues. Importantly, actin cytoskeleton, which propagates actomyosin contractile forces, forms several characteristic structures in a 3D intracellular space, such as a circumferential actin belt lining adherence junctions and an actin mesh beneath the apical membrane. However, little is known about how epithelial mechanical property depends on the intracellular contractile structures. We performed computational simulations using a 3D vertex model, and demonstrated the longitudinal tensile test of an epithelial tube, whose inside and outside are defined as the apical and basal surfaces, respectively. As a result, these subcellular structures provide the contrary dependence of epithelial stiffness and fracture force on the spontaneous curvature of constituent cells; the epithelial stiffness increases with increasing the spontaneous curvature in the case of belt, meanwhile it decreases in the case of mesh. This qualitative difference emerges from the different anisotropic deformability of apical cell surfaces; while belt preserves isotropic apical cell shapes, mesh does not. Moreover, the difference in the anisotropic deformability determines the frequency of cell rearrangements, which in turn effectively decrease the tube stiffness. These results illustrate the importance of the intracellular contractile structures, which may be regulated to optimize mechanical functions of individual epithelial tissues.

Self-organizing optic-cup morphogenesis in three-dimensional culture.

Balanced organogenesis requires the orchestration of multiple cellular interactions to create the collective cell behaviours that progressively shape developing tissues. It is currently unclear how individual, localized parts are able to coordinate with each other to develop a whole organ shape. Here we report the dynamic, autonomous formation of the optic cup (retinal primordium) structure from a three-dimensional culture of mouse embryonic stem cell aggregates. Embryonic-stem-cell-derived retinal epithelium spontaneously formed hemispherical epithelial vesicles that became patterned along their proximal-distal axis. Whereas the proximal portion differentiated into mechanically rigid pigment epithelium, the flexible distal portion progressively folded inward to form a shape reminiscent of the embryonic optic cup, exhibited interkinetic nuclear migration and generated stratified neural retinal tissue, as seen in vivo. We demonstrate that optic-cup morphogenesis in this simple cell culture depends on an intrinsic self-organizing program involving stepwise and domain-specific regulation of local epithelial properties.

Numerical assessment of the applicability of geometry-based force inference on homogeneous and heterogeneous cells.

The measurement of cellular forces, which reflect crucial biological attributes, has the potential to replace conventional cell assessment methods, such as morphology, proliferation, and molecular expression analysis, in medical cell diagnosis and cell culture studies. In medical cell evaluations, force inference techniques have gained prominence due to their non-invasiveness and lack of requirement for specialized equipment. Among those techniques, the method proposed by Ishihara et al., which estimates forces in densely packed cells based only on cell geometry, is a promising method. However, its applicability range of this method has not been fully established. In this study, we employed a two-dimensional vertex model to numerically assess the applicability of this method on homogeneous and heterogeneous cells. Our comparisons between the true values from numerical simulations and the estimated values from the inference method revealed a significant correlation between estimation accuracy and cell roundness in systems of homogeneous cell. Moreover, the method demonstrated efficient force estimations in heterogeneous-cell systems. These findings may be useful when the force inference method is employed to evaluate medical cells.

Long-term adherent cell dynamics emerging from energetic and frictional interactions at the interface.

Cell adhesion plays an important role in a wide range of biological situations, including embryonic development, cancer invasion, and wound healing. Although several computational models describing adhesion dynamics have been proposed, models applicable to long-term, large-length-scale cell dynamics are lacking. In this study we investigated possible states of long-term adherent cell dynamics in three-dimensional space by constructing a continuum model of interfacial interactions between adhesive surfaces. In this model a pseudointerface is supposed between each pair of triangular elements that discretize cell surfaces. By introducing a distance between each pair of elements, the physical properties of the interface are given by interfacial energy and friction. The proposed model was implemented into the model of a nonconservative fluid cell membrane where the cell membrane dynamically flows with turnover. Using the implemented model, numerical simulations of adherent cell dynamics on a substrate under flow were performed. The simulations not only reproduced the previously reported dynamics of adherent cells, such as detachment, rolling, and fixation on the substrate, but also discovered other dynamic states, including cell slipping and membrane flow patterns, corresponding to behaviors that occur on much longer timescales than the dissociation of adhesion molecules. These results illustrate the variety of long-term adherent cell dynamics, which are more diverse than the short-term ones. The proposed model can be extended to arbitrarily shaped membranes, thus being useful for the mechanical analysis of a wide range of long-term cell dynamics where adhesion is essential.

Machine learning-based estimation of spatial gene expression pattern during ESC-derived retinal organoid development.

Organoids, which can reproduce the complex tissue structures found in embryos, are revolutionizing basic research and regenerative medicine. In order to use organoids for research and medicine, it is necessary to assess the composition and arrangement of cell types within the organoid, i.e., spatial gene expression. However, current methods are invasive and require gene editing and immunostaining. In this study, we developed a non-invasive estimation method of spatial gene expression patterns using machine learning. A deep learning model with an encoder-decoder architecture was trained on paired datasets of phase-contrast and fluorescence images, and was applied to a retinal organoid derived from mouse embryonic stem cells, focusing on the master gene Rax (also called Rx), crucial for eye field development. This method successfully estimated spatially plausible fluorescent patterns with appropriate intensities, enabling the non-invasive, quantitative estimation of spatial gene expression patterns within each tissue. Thus, this method could lead to new avenues for evaluating spatial gene expression patterns across a wide range of biology and medicine fields.

Actin crosslinking by α-actinin averts viscous dissipation of myosin force transmission in stress fibers.

Contractile force generated in actomyosin stress fibers (SFs) is transmitted along SFs to the extracellular matrix (ECM), which contributes to cell migration and sensing of ECM rigidity. In this study, we show that efficient force transmission along SFs relies on actin crosslinking by α-actinin. Upon reduction of α-actinin-mediated crosslinks, the myosin II activity induced flows of actin filaments and myosin II along SFs, leading to a decrease in traction force exertion to ECM. The fluidized SFs maintained their cable integrity probably through enhanced actin polymerization throughout SFs. A computational modeling analysis suggested that lowering the density of actin crosslinks caused viscous slippage of actin filaments in SFs and, thereby, dissipated myosin-generated force transmitting along SFs. As a cellular scale outcome, α-actinin depletion attenuated the ECM-rigidity-dependent difference in cell migration speed, which suggested that α-actinin-modulated SF mechanics is involved in the cellular response to ECM rigidity.

Multicellular dynamics on structured surfaces: Stress concentration is a key to controlling complex microtissue morphology on engineered scaffolds.

Tissue engineers have utilised a variety of three-dimensional (3D) scaffolds for controlling multicellular dynamics and the resulting tissue microstructures. In particular, cutting-edge microfabrication technologies, such as 3D bioprinting, provide increasingly complex structures. However, unpredictable microtissue detachment from scaffolds, which ruins desired tissue structures, is becoming an evident problem. To overcome this issue, we elucidated the mechanism underlying collective cellular detachment by combining a new computational simulation method with quantitative tissue-culture experiments. We first quantified the stochastic processes of cellular detachment shown by vascular smooth muscle cells on model curved scaffolds and found that microtissue morphologies vary drastically depending on cell contractility, substrate curvature, and cell-substrate adhesion strength. To explore this mechanism, we developed a new particle-based model that explicitly describes stochastic processes of multicellular dynamics, such as adhesion, rupture, and large deformation of microtissues on structured surfaces. Computational simulations using the developed model successfully reproduced characteristic detachment processes observed in experiments. Crucially, simulations revealed that cellular contractility-induced stress is locally concentrated at the cell-substrate interface, subsequently inducing a catastrophic process of collective cellular detachment, which can be suppressed by modulating cell contractility, substrate curvature, and cell-substrate adhesion. These results show that the developed computational method is useful for predicting engineered tissue dynamics as a platform for prediction-guided scaffold design. STATEMENT OF SIGNIFICANCE: Microfabrication technologies aiming to control multicellular dynamics by engineering 3D scaffolds are attracting increasing attention for modelling in cell biology and regenerative medicine. However, obtaining microtissues with the desired 3D structures is made considerably more difficult by microtissue detachments from scaffolds. This study reveals a key mechanism behind this detachment by developing a novel computational method for simulating multicellular dynamics on designed scaffolds. This method enabled us to predict microtissue dynamics on structured surfaces, based on cell mechanics, substrate geometry, and cell-substrate interaction. This study provides a platform for the physics-based design of micro-engineered scaffolds and thus contributes to prediction-guided biomaterials design in the future.

Intestinal and optic-cup organoids as tools for unveiling mechanics of self-organizing morphogenesis.

Organoid, an organ-like tissue reproduced in a dish, has specialized, functional structures in three-dimensional (3D) space. Organoid development replicates the self-organizing process of each tissue development during embryogenesis but does not necessarily require external tissues, illustrating the autonomy of multicellular systems. Herein, we review the developmental processes of epithelial organoids, namely, the intestine, and optic-cup, with a focus on their mechanical aspects. Recent organoid studies have advanced our understanding of the mechanisms of 3D tissue deformation, including appropriate modes of deformation and factors controlling them. In addition, the autonomous nature of organoid development has also allowed us to access the stepwise mechanisms of deformation as organoids proceed through distinct stages of development. Altogether, we discuss the potential of organoids in unveiling the autonomy of multicellular self-organization from a mechanical point of view. This review article is an extended version of the Japanese article, Mechanics in Self-organizing Organoid Morphogenesis, published in SEIBUTSU BUTSURI Vol. 60, p.31-36 (2020).

Src activation in lipid rafts confers epithelial cells with invasive potential to escape from apical extrusion during cell competition.

Abnormal/cancerous cells within healthy epithelial tissues undergo apical extrusion to protect against carcinogenesis, although they acquire invasive capacity once carcinogenesis progresses. However, the molecular mechanisms by which cancer cells escape from apical extrusion and invade surrounding tissues remain elusive. In this study, we demonstrate a molecular mechanism for cell fate switching during epithelial cell competition. We found that during competition within epithelial cell layers, Src transformation promotes maturation of focal adhesions and degradation of extracellular matrix. Src-transformed cells underwent basal delamination by Src activation within sphingolipid/cholesterol-enriched membrane microdomains/lipid rafts, whereas they were apically extruded when Src was outside of lipid rafts. A comparative analysis of contrasting phenotypes revealed that activation of the Src-STAT3-MMP axis through lipid rafts was required for basal delamination. CUB-domain-containing protein 1 (CDCP1) was identified as an Src-activating scaffold and as a Met regulator in lipid rafts, and its overexpression induced basal delamination. In renal cancer models, CDCP1 promoted epithelial-mesenchymal transition-mediated invasive behavior by activating the Src-STAT3-MMP axis through Met activation. Overall, these results suggest that spatial activation of Src signaling in lipid rafts confers resistance to apical extrusion and invasive potential on epithelial cells to promote carcinogenesis.

Nano-scale physical properties characteristic to metastatic intestinal cancer cells identified by high-speed scanning ion conductance microscope.

Recent genetic studies have indicated relationships between gene mutations and colon cancer phenotypes. However, how physical properties of tumor cells are changed by genetic alterations has not been elucidated. We examined genotype-defined mouse intestinal tumor-derived cells using a high-speed scanning ion conductance microscope (HS-SICM) that can obtain high-resolution live images of nano-scale topography and stiffness. The tumor cells used in this study carried mutations in Apc (A), Kras (K), Tgfbr2 (T), Trp53 (P), and Fbxw7 (F) in various combinations. Notably, high-metastatic cancer-derived cells carrying AKT mutations (AKT, AKTP, and AKTPF) showed specific ridge-like morphology with active membrane volume change, which was not found in low-metastatic and adenoma-derived cells. Furthermore, the membrane was significantly softer in the metastatic AKT-type cancer cells than other genotype cells. Importantly, a principal component analysis using RNAseq data showed similar distributions of expression profiles and physical properties, indicating a link between genetic alterations and physical properties. Finally, the malignant cell-specific physical properties were confirmed by an HS-SICM using human colon cancer-derived cells. These results indicate that the HS-SICM analysis is useful as a novel diagnostic strategy for predicting the metastatic ability of cancer cells.

Marcksl1 modulates endothelial cell mechanoresponse to haemodynamic forces to control blood vessel shape and size.

The formation of vascular tubes is driven by extensive changes in endothelial cell (EC) shape. Here, we have identified a role of the actin-binding protein, Marcksl1, in modulating the mechanical properties of EC cortex to regulate cell shape and vessel structure during angiogenesis. Increasing and depleting Marcksl1 expression level in vivo results in an increase and decrease, respectively, in EC size and the diameter of microvessels. Furthermore, endothelial overexpression of Marcksl1 induces ectopic blebbing on both apical and basal membranes, during and after lumen formation, that is suppressed by reduced blood flow. High resolution imaging reveals that Marcksl1 promotes the formation of linear actin bundles and decreases actin density at the EC cortex. Our findings demonstrate that a balanced network of linear and branched actin at the EC cortex is essential in conferring cortical integrity to resist the deforming forces of blood flow to regulate vessel structure.

Wall boundary model for primitive chain network simulations.

In condensed polymeric liquids confined in slit channels, the movement of chains is constrained by two factors: entanglement among the chains and the excluded volume between the chains and the wall. In this study, we propose a wall boundary (WB) model for the primitive chain network (PCN) model, which describes the dynamics of polymer chains in bulk based on coarse graining upon the characteristic molecular weight of the entanglement. The proposed WB model is based on the assumptions that (i) polymers are not stuck but simply reflected randomly by the wall, and (ii) subchains below the entanglement length scale behave like those in bulk even near the wall. Using the WB model, we simulate the dynamics of entangled polymer chains confined in slit channels. The results show that as the slit narrows, the chains are compressed in the direction normal to the wall, while they are expanded in the parallel direction. In addition, the relaxation time of the end-to-end vector increases, and the diffusivity of the center of mass decreases. The compression in the normal direction is a natural effect of confinement, while the expansion is introduced by a hooking process near the wall. The trends revealed that the relaxation time and diffusivity depend on the increase in friction due to an increased number of entanglements near the wall, which is also associated with the hooking process in the PCN model. These results are expected within the assumptions of the PCN model. Thus, the proposed WB model can successfully reproduce the effects of wall confinement on chains.