## 1 Introduction 

Complex gene regulatory or protein networks are responsible for determining cellu- lar behaviors. The function of such networks has recently been discussed in the light of specific network structures called network motifs (Shen-Orr et al., 2002; Milo et al., 2002, 2004). Besides such motifs, several simple network modules are also considered to op- erate to give specific dynamical properties such as bistability, adaptation, or oscillatory behavior (Ferrell Jr. and Machleder, 1998; Sha et al., 2003; Tyson et al., 2003). Recent experimental results also suggest that such modules provide a basis for cell differentiation, as studied in competence state in Bacillus subtilis (S¨ uel et al., 2006; Maamar et al., 2007). 

In multicellular organisms, several cell states coexist. Morphogenesis with differen- tiation into distinct cell types, however, is not an event of independent single-cellular dynamics, but occurs as a result of an ensemble of interacting cells. For determining each cell type, cell-cell interactions are often essential besides intra-cellular dynamics by functional modules at a single cell level. In fact, gene regulatory networks respon- sible for the early developmental process or the cell specification process of several kinds of organisms include many intercellular interactions (Ben-Tabou de-Leon and Davidson, 2007; E. H. Davidson et al., 2002; Imai et al., 2006; Loose and Patient, 2004; Swiers et al., 2006). The importance of cell-cell interactions to robust developmental processes is dis- cussed as the community effect (Gurdon et al., 1993) and differentiation from equivalent groups of cells (Greenwald and Rubin, 1992). 

When considering the development of a multi-cellular organism, not only a set of cell types, but also the number distribution of each of the cell types, has to be suitably deter- mined and robust against perturbations during the course of development. The proportion of the body plan in planarian and in the slug of Dictyostelium discoideum is preserved over a wide range of body sizes (Oviedo et al., 2003; R` afols et al., 2000). In the D. discoideum slug, the number ratio of two cell types is kept almost constant. In the hematopoietic sys- tem of mammals approximately ten different cell types are generated from a hematopoietic 

