which is a candidate for the involvement in the niche-stem interaction, disappears after commitment to the lymphoid lineage (Radtke et al., 2004). The differentiation in the hematopoietic system may correspond to that studied in model II. Thirdly, an example for model III is given by the proportion regulation of prestalk- cell types and prespore-cell types in the Dictyostelium slug. Differentiation to prespore cells is induced by cAMP, and the cell state is maintained by a positive-feedback loop of prespore cell specific adenylyl cyclase G activity (Hopper et al., 1993; Williams, 2006; Alvarez-Curto et al., 2007). On the other hand, differentiation-inducing factor-1 (DIF- 1) is necessary for the differentiation from a prespore-cell to a prestalk-cell (at least for the differentiation to pstO which is a subtype of the prestalk-cell) (Williams, 2006; Kay and Thompson, 2001). As an intercellular interaction, this DIF-1 is produced by prespore-cells, and are degraded by prestalk-cells. This cell-type specific induction/destruction of DIF-1 is responsible for the proportion preservation as studied in model III. Although we confine our analysis to a system with only fixed point solutions, oscilla- tory and other dynamical behaviors are often observed in biological systems. The analysis we introduced here is also applicable to such cases, as long as there are bifurcations of attractors with the change in relevant chemical concentrations which are influenced by cell-cell interactions. On the other hand, oscillatory behaviors may bring about richer bi- furcations, as well as clustering of cells with regards to the oscillation phase or amplitude, as has been discussed in models with intra-cellular oscillatory dynamics and cell-cell in- teractions (Kaneko and Yomo, 1994, 1997; Koseska et al., 2007; Ullner et al., 2007). The study of possible forms on differentiations and regulations in such dynamical systems will be important in future. In multicellular systems, cells behave in coordination by taking advantage of communication with other cells. Such collective behavior is a result of inter- acting systems with intra-cellular gene expression dynamics. The present self-consistent determination of bifurcation parameters through cell-cell interactions will be essential to understand organization in multicellularity. 16