An analytical study of the number of steady states in gene regulatory networks

Herein, I proposed a model for gene networks and studied the steady states in the dynamics both by numerical and analytical methods. In this model, mRNA and protein levels change continuously with time; each gene alters transcriptional regulation depending on the concentration of transcription factors. The dynamical behavior of continuous model is quite complex and different from that of the discrete model, the Boolean network. Large portion of steady states of this model can be classified into three types. The rough structure of gene interactions, which corresponds to Boolean function, is sufficient to predict the expression level of each gene in these types of steady states. I also determined the expected numbers of two major types of steady states observed in a randomly generated gene network. The results obtained from these formulae contradict previously accepted belief. The results are that neither gene number nor connectivity between genes increases the expected number of steady states in a random gene network. The number of steady states is very small. The number of self-regulatory genes, however, effectively increases the number of steady states in a network. These results imply that increases in gene number may not be the direct driving force for the evolution of a variety of different cell types within organisms. Instead, the number of self-regulatory genes may significantly increase cellular diversity.