transition from the single-cluster state of u$_{(1)}$ to a two-cluster state occurs by the increase in the total cell number. In model II, the cell-type 2 contributes only weakly to the increase of v , compared with the cell-type 1. Thus, the amount of v mainly depends on the number of the cell-type 1. In contrast, in model III, the cell-type 2 degrades v . As a result, the amount of v depends on the number ratio of two cell-types. 

If a gene expression network shows bistability with a bifurcation structure as in Fig. 1, cell differentiation is a general consequence when cell-cell couplings are introduced. An important point here is that the same intracellular module can be used in several different biological contexts by modifying only the intercellular interaction. This is quite useful in an evolutionary perspective because new biological functions can be added by incorporat- ing new interactions while preserving the intracellular core module. 

Here, we discuss several biological examples that may correspond to our models. First, we refer to the cell cycle machinery in Xenopus , where a Cdc2 positive feedback loop makes a bifurcation with regards to the amount of cyclin B, and introduces bistability as in Fig. 1. In this system, an increase in the DNA amount in the early embryo induces the transi- tion from the low Tyr15 phosphorylation state of Cdc2 to the high Tyr15 phosphorylation state, which seems to cause the mid-blastula transition in Xenopus (Novak and Tyson, 1993; Hartley et al., 1996; Sha et al., 2003). The induced differentiation may correspond to that observed in model I. 

Secondly, as for model II, consider the maintenance of the hematopoietic stem cells in mammals, where osteoblasts work as a stem cell niche (Calvi, 2006). The stem cells compete for some chemical factor representing this niche, and the cells which cannot take the factor differentiate to specific hematopoietic lineages. It has been discussed that the regulation of the stem cell population size is realized through the competition for the fac- tor, to which responsibility decreases through the differentiation process (Radtke et al., 2004; Adams and Scadden, 2006). Indeed, it is observed that the expression of Notch1, 

