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

Abstract

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.