Robust and Irreversible Development in Cell Society as a General Consequence of Intra-Inter Dynamics

A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and rules for differentiation are found as a natural consequence of such a system. “Stem cells” that either proliferate or differentiate to different types stochastically are found to appear when intra-cellular dynamics are chaotic. Robustness of the developmental process against microscopic and macroscopic perturbations is shown to be a natural consequence of such intra-inter dynamics, while irreversibility in developmental process is discussed in terms of the gain of stability, loss of diversity and chaotic instability. 1 Intra-inter Dynamics for Cell Biology A biological unit has always some internal structure that can change in time. These units, however, are not separated from the outside world completely. For example, consider a cell. In this case, isolation by a biomembrane is flexible and incomplete. When the units are represented by dynamical systems, they interact with each other and with the external environment. Hence, we need a model consisting of the interplay between inter-unit and intra-unit