Structure of regulatory networks and diversity of gene expression patterns.

Complexity of gene regulatory network has been considered to be responsible for diversity of cells. Different types of cells, characterized by the expression patterns of genes, are produced in early development through the dynamics of gene activities based on the regulatory network. However, very little is known about relationship between the structure of regulatory networks and the dynamics of gene activities. In this paper, I introduce new idea of "steady-state compatibility" by which the diversity of possible gene activities can be determined from the topological structure of gene regulatory networks. The basic premise is very simple: the activity of a gene should be a function of the controlling genes. Thus, a gene should always show unique expression activity if the activities of the controlling genes are unique. Based on this, the maximum possible diversity of steady states is determined using only information regarding regulatory linkages without knowing the regulatory functions of genes. By extending this idea, some general properties were derived. For example, multiple loop structures in regulatory networks are necessary for increasing the diversity of gene activity. On the other hand, connected multiple loops sharing the same genes do not increase the diversity. The method was applied to a gene regulatory network responsible for early development in a sea urchin species. A set of important genes responsible for generating diversities of gene activities was derived based on the concept of compatibility of steady states.