Among morphological phenomena, cellular patterns in developing sensory epithelia have gained attention in recent years. Although physical models for cellular rearrangements are well-established thanks to a large bulk of experimental work, their computational implementation lacks solid mathematical background and involves experimentally unreachable parameters. Here we introduce a level set-based computational framework as a tool to rigorously investigate evolving cellular patterns, and study its mathematical and computational properties. We illustrate that a compelling feature of the method is its ability to correctly handle complex topology changes, including frequent cell intercalations. Combining this accurate numerical scheme with an established mathematical model, we show that the proposed framework features minimum possible number of parameters and is capable of reproducing a wide range of tissue morphological phenomena, such as cell sorting, engulfment or internalization. In particular, thanks to precise mathematical treatment of cellular intercalations, this method succeeds in simulating experimentally observed development of cellular mosaic patterns in sensory epithelia.

Applied Mathematics and Informatics Course Faculty of Advanced Science and Technology Ryukoku University Otsu Japan

Department of Biochemistry and Molecular Biology Kobe University Graduate School of Medicine Kobe Japan

Department of Mathematics Graduate School of Science Kyoto University Kyoto Japan

Institute of Mathematics College of Science University of the Philippines Diliman Quezon City Philippines

JST PRESTO Kobe Japan

Mathematical Institute Czech Academy of Sciences Prague Czech Republic

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A numerical algorithm for modeling cellular rearrangements in tissue morphogenesis

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