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

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