Dynamics maintaining diversity
of cell types in a
multi-cellular
system are studied in
relationship with the plasticity of cellular states. First, we
introduce a new theoretical framework,
reaction-diffusion
system on `chemical
species space' to model intra-cellular chemical reaction dynamics.
Then, by considering the cell division and death of such cells,
developmental process from a single cell is studied. Cell
differentiation
process is found to occur
through instability in transient dynamics and cell-cell interaction.
In a long time 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 large
extinction
, from which diversity and plasticity
are recovered. After this switching, decrease of plasticity again
occurs, leading to the next extinction of multiple cells. This
cycle of diversification and extinction is repeated. Relevance of
our results to the development and evolution is briefly discussed.