"Cellular patterning in sensory systems: An interface evolution problem"
This work in collaboration with Karel Svadlenka (Kyoto University), Hideru Togashi (Kobe University), and Hideki Murakawa (Ryukoku University) focuses on modeling cellular rearrangements in tissue morphogenesis, with emphasis on observed cellular pattern formations in sensory epithelia. Adopting the viewpoint of free energy minimization principle, we focus on the energy associated with cell-cell junction, an interface between cells. We take cellular rearrangement as an $L^2$-gradient flow of a weighted interfacial energy constrained by each cell's preferred volume, where the weights are related to physical parameters of the cells, for example, cell-cell adhesion and cell contractility. Unlike existing models such as vertex dynamics model and cellular Potts model, which are also based on free energy minimization, we propose a level set-based approach which allows for cell-cell junctions with nonzero curvatures, realizes the correct cell contact angles, has minimal possible number of parameters, and naturally handles topological changes, e.g., cell intercalation, without relying on ad hoc algorithms that inevitably involve unnatural parameters. This model successfully reproduces the development of cellular patterns in embryonic auditory and olfactory epithelial tissues.