Dynamical systems basis of metamorphosis: diversity and plasticity of cellular states in reaction diffusion network

Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relation to the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics and considering the division and death of cells, the development of cells is studied. Cell differentiation process is found to occur through instability in transient dynamics and cell-cell interaction. In long-term behavior, extinction of multiple cells is repeated, which leads to itinerancy over successive quasi-stable multi-cellular states consisting of different types of cells. By defining the plasticity of a cellular state, it is shown that the plasticity of cells decreases before the extinction of most cell types, from which diversity and plasticity are later recovered. In the following, a decrease of plasticity occurs again, leading to the next extinction. This cycle of diversification and extinction is repeated. Relevance of our results to development and evolution is briefly discussed.