# Regulative Differentiation as Bifurcation of Interacting Cell Population 

Akihiko Nakajima $^{1}$, Kunihiko Kaneko1 , 2 

$^{1}$Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan 

$^{2}$ERATO Complex Systems Biology Project, JST, Japan 

Corresponding author: Akihiko Nakajima 

E-mail address: nakajima@complex.u-tokyo.ac.jp 

Tel./fax: +81 3 5454 6732. 

In multicellular organisms, several cell states coexist. For determining each cell type, cell-cell interactions are often essential, in addition to intracellular gene expression dynam- ics. Based on dynamical systems theory, we propose a mechanism for cell differentiation with regulation of populations of each cell type by taking simple cell models with gene expression dynamics. By incorporating several interaction kinetics, we found that the cell models with a single intracellular positive-feedback loop exhibit a cell fate switching, with a change in the total number of cells. The number of a given cell type or the population ratio of each cell type is preserved against the change in the total number of cells, de- pending on the form of cell-cell interaction. The differentiation is a result of bifurcation of cell states via the intercellular interactions, while the population regulation is explained by self-consistent determination of the bifurcation parameter through cell-cell interactions. The relevance of this mechanism to development and differentiation in several multicellular systems is discussed. 

