Analysis of a Minimal Gene Regulatory Network for Cell Differentiation

In this letter, we provide a detailed analysis of a gene regulatory network exhibiting bistability within a certain region of parameter space. This network has been adopted in recent literature to describe cellular differentiation into two subpopulations. Biological and experimental evidence suggests that differentiation from stem cells into different tissues evolves through a cascade of similar stages characterized by differentiation into two subtypes. Each differentiation step is influenced by two mechanisms: the first one occurs within the cell and allows transition from an undifferentiated stage to a pluripotent stage where differentiation is possible and the second mechanism may be external to the cell and biases differentiation into a specific subpopulation. In this letter, we address the former mechanism for a gene circuit described by generalized Hill equations and endowed with mutual inhibitory feedback among two competing genes. The main contribution is twofold: 1) mutual inhibition is not sufficient to allow cell differentiation, but specific conditions on the generalized Hill equations’ parameters are required and 2) differentiation occurs only if the triggering gene expression level belongs to a well defined range. Theoretical analysis is complemented with numerical simulations.