Satoru Okuda

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.

Modeling cell proliferation for simulating three-dimensional tissue morphogenesis based on a reversible network reconnection framework

Tissue morphogenesis in multicellular organisms is accompanied by proliferative cell behaviors: cell division (increase in cell number after each cell cycle) and cell growth (increase in cell volume during each cell cycle). These proliferative cell behaviors can be regulated by multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze multicellular dynamics, a reversible network reconnection (RNR) model has been suggested, in which each cell shape is expressed by a single polyhedron. In this study, to apply the RNR model to simulate tissue morphogenesis involving proliferative cell behaviors, we model cell proliferation based on a RNR model framework. In this model, cell division was expressed by dividing a polyhedron at a planar surface for which cell division behaviors were characterized by three quantities: timing, intracellular position, and normal direction of the dividing plane. In addition, cell growth was expressed by volume growth as a function of individual cell times within their respective cell cycles. Numerical simulations using the proposed model showed that tissues grew during successive cell divisions with several cell cycle times. During these processes, the cell number in tissues increased while maintaining individual cell size and shape. Furthermore, tissue morphology dramatically changed based on different regulations of cell division directions. Thus, the proposed model successfully provided a basis for expressing proliferative cell behaviors during morphogenesis based on a RNR model framework.

Reversible network reconnection model for simulating large deformation in dynamic tissue morphogenesis

Morphogenesis of tissues in organ development is accompanied by large three-dimensional (3D) deformations, in which mechanical interactions among multiple cells are spatiotemporally regulated. To reveal the deformation mechanisms, in this study, we developed the reversible network reconnection (RNR) model. The model is developed on the basis of 3D vertex model, which expresses a multicellular aggregate as a network composed of vertices. 3D vertex models have successfully simulated morphogenetic dynamics by expressing cellular rearrangements as network reconnections. However, the network reconnections in 3D vertex models can cause geometrical irreversibility, energetic inconsistency, and topological irreversibility, therefore inducing unphysical results and failures in simulating large deformations. To resolve these problems, we introduced (1) a new definition of the shapes of polygonal faces between cellular polyhedrons, (2) an improved condition for network reconnections, (3) a new condition for potential energy functions, and (4) a new constraint condition for the shapes of polygonal faces that represent cell–cell boundaries. Mathematical and computational analyses demonstrated that geometrical irreversibility, energetic inconsistency, and topological irreversibility were resolved by suppressing the geometrical gaps in the network and avoiding the generation of irreversible network patterns in reconnections. Lastly, to demonstrate the applicability of the RNR model, we simulated tissue deformation of growing cell sheets and showed that our model can simulate large tissue deformations, in which large changes occur in the local curvatures and layer formations of tissues. Thus, the RNR model enables in silico recapitulation of complex tissue morphogenesis.

Vertex dynamics simulations of viscosity-dependent deformation during tissue morphogenesis

In biological development, multiple cells cooperate to form tissue morphologies based on their mechanical interactions; namely active force generation and passive viscoelastic response. In particular, the dynamic processes of tissue deformations are governed by the viscous properties of the tissues. These properties are spatially inhomogeneous because they depend on the tissue constituents, such as cytoplasm, cytoskeleton, basement membrane and extracellular matrix. The multicellular mechanics of tissue morphogenesis have been investigated in vertex dynamics models. However, conventional models are applicable only to quasi-static deformation processes, which do not account for tissue viscosities. We propose a vertex dynamics model that simulates the viscosity-dependent dynamic deformation processes during tissue morphogenesis. By incorporating local velocity fields into the governing equation of vertex movements, the model turns Galilean invariant. In addition, the viscous properties of tissue components are newly expressed by formulating friction forces on vertices as functions of the relative velocities among the vertices. The advantages of the proposed model are examined by epithelial growth simulations under the employed condition for quasi-static processes. As a result, the epithelial vesicle simulated by the proposed model is linearly elongated with nearly free stress, while that simulated by the conventional model is undulated with compressive residual stress. Therefore, the proposed model is able to reflect the timescale of deformations by satisfying Galilean invariance. Next, the applicability of the proposed model is assessed in epithelial growth simulations of viscous extracellular materials. In this test, the epithelial vesicles are deformed into tubular shapes by oriented cell divisions, and their morphologies are extremely sensitive to extracellular viscosity. Therefore, the dynamic deformations in the proposed model depend on the viscous properties of tissue components. The proposed model will be useful for simulating dynamic deformation processes of tissue morphogenesis depending on viscous properties of various tissue components.

Apical contractility in growing epithelium supports robust maintenance of smooth curvatures against cell-division-induced mechanical disturbance.

In general, a rapidly growing epithelial sheet during tissue morphogenesis shows a smooth and continuous curvature on both inner cavity (apical) and basement membrane (basal) sides. For instance, epithelia of the neural tube and optic vesicle in the early embryo maintain continuous curvatures in their local domains, even during their rapid growth. However, given that cell divisions, which substantially perturb the local force balance, frequently and successively occur in an uncoordinated manner, it is not self-evident to explain how the tissue keeps a continuous curvature at large. In the majority of developing embryonic epithelia with smooth surfaces, their curvatures are apically concave, because of the presence of strong tangential contractile force on the apical side. In this numerical study, we demonstrate that tangential contractile forces on the apical surface play a critical role in the maintenance of smooth curvatures in the epithelium and reduce irregular undulations caused by uncoordinated generation of local pushing force. Using a reversible network reconnection (RNR) model, which we previously developed to make numerical analyses highly reproducible even under rapid tissue-growth conditions, we performed simulations for morphodynamics to examine the effect of apical contractile forces on the continuity of curvatures. Interestingly, the presence of apical contractile forces suppressed irregular undulations not only on the apical side but also on the basal surface. These results indicate that cellular contractile forces on the apical surface control not only the shape at a single cell level but also at a tissue level as a result of emergent mechanical coordination.

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. Highlighted article: Intrinsic mechanisms involving the spatiotemporal regulation of canonical Wnt and BMP signals play a role in setting up DV polarity in mouse ESC-derived optic cups.

Coupling intercellular molecular signalling with multicellular deformation for simulating three-dimensional tissue morphogenesis.

During morphogenesis, three-dimensional (3D) multicellular structures emerge from biochemical and mechanical interplays among cells. In particular, by organizing their gradient within tissues, the diffusible signalling molecules play an essential role in producing the spatio-temporal patterns of cell status such as the differentiation states. Notably, this biochemical patterning can be dynamically coupled with multicellular deformations by signal-dependent cell activities such as contraction, adhesion, migration, proliferation and apoptosis. However, the mechanism by which these cellular activities mediate the interactions between multicellular deformations and patterning is still unknown. Herein, we propose a novel framework of a 3D vertex model to express molecular signalling among the mechanically deforming cells. By specifying a density of signalling molecules for each cell, we express their transport between neighbouring cells. By simulating signal-dependent epithelial growth, we found various types of tissue morphogenesis such as arrest, expansion, invagination and evagination. In the expansion phase, growth molecules were widely diffused with increasing tissue volume, which diluted the growth molecules in order to support the autonomous suppression of tissue growth. These results indicate that the proposed model successfully expresses 3D multicellular deformations dynamically coupled with biochemical patterning. We expect our proposed model to be a useful tool for predicting new phenomena emerging from mechanochemical coupling in multicellular morphogenesis.

Three-dimensional vertex model for simulating multicellular morphogenesis

During morphogenesis, various cellular activities are spatiotemporally coordinated on the protein regulatory background to construct the complicated, three-dimensional (3D) structures of organs. Computational simulations using 3D vertex models have been the focus of efforts to approach the mechanisms underlying 3D multicellular constructions, such as dynamics of the 3D monolayer or multilayer cell sheet like epithelia as well as the 3D compacted cell aggregate, including dynamic changes in layer structures. 3D vertex models enable the quantitative simulation of multicellular morphogenesis on the basis of single-cell mechanics, with complete control of various cellular activities such as cell contraction, growth, rearrangement, division, and death. This review describes the general use of the 3D vertex model, along with its applications to several simplified problems of developmental phenomena.

Modeling cell apoptosis for simulating three-dimensional multicellular morphogenesis based on a reversible network reconnection framework.

Morphogenesis in multicellular organisms is accompanied by apoptotic cell behaviors: cell shrinkage and cell disappearance. The mechanical effects of these behaviors are spatiotemporally regulated within multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze 3D multicellular dynamics, 3D vertex models have been suggested, in which a reversible network reconnection (RNR) model has successfully expressed 3D cell rearrangements during large deformations. To analyze the effects of apoptotic cell behaviors on 3D multicellular morphogenesis, we modeled cell apoptosis based on the RNR model framework. Cell shrinkage was modeled by the potential energy as a function of individual cell times during the apoptotic phase. Cell disappearance was modeled by merging neighboring polyhedrons at their boundary surface according to the topological rules of the RNR model. To establish that the apoptotic cell behaviors could be expressed as modeled, we simulated morphogenesis driven by cell apoptosis in two types of tissue topology: 3D monolayer cell sheet and 3D compacted cell aggregate. In both types of tissue topology, the numerical simulations successfully illustrated that cell aggregates gradually shrank because of successive cell apoptosis. During tissue shrinkage, the number of cells in aggregates decreased while maintaining individual cell size and shape. Moreover, in case of localizing apoptotic cells within a part of the 3D monolayer cell aggregate, the cell apoptosis caused the global tissue bending by pulling on surrounding cells. In case of localizing apoptotic cells on the surface of the 3D compacted cell aggregate, the cell apoptosis caused successive, directional cell rearrangements from the inside to the surface. Thus, the proposed model successfully provided a basis for expressing apoptotic cell behaviors during 3D multicellular morphogenesis based on an RNR model framework.

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.