Yoshida, Hiroshi, Chikara Furusawa, and Kunihiko Kaneko. “Selection of initial conditions for recursive production of multicellular organisms.” Journal of theoretical biology 233, no. 4 (2005): 501-514.
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The development of a multicellular organism is a dynamic process. Starting from one or a few cells, the organism becomes a set of cells with different types that form well-determined patterns. It is rather surprising that differentiation in cell types and formation of controlled patterns are compatible, because the former gives morphogenetic diversification whereas the latter implies recursive production of a cell ensemble, reducing individual differences. We studied this problem by taking a simple cell model with intracellular reaction dynamics of chemical concentrations, cell–cell interactions, and increase in cell numbers. We observed successive differentiation from a cell type with diverse chemicals and chaotic concentration dynamics to cell types with oscillatory or fixed-point dynamics, leading to morphogenetic diversity in a spatial pattern. We further show that, by starting from an initial object consisting of both the former cell type with diverse chemicals and the latter differentiated cell type, the recursive production of a multicellular organism with morphogenetic diversity is possible. By relating the former type to a cell in the vegetal pole and the latter to one in the animal pole, classic experimental results with separation of blastomeres in sea urchin eggs are coherently explained, while some predictions are made for in vitro morphogenesis from embryonic stem cells.