Spatial Differentiation and Positive Circuits in a Discrete Framework

Abstract. The biologist R. Thomas has enounced a rule relating multistationnarity in a system of genes interacting in a single cell to the existence of a positive circuit in the regulatory graph. In this paper, we address the question of a similar Thomas' rule for spatial differentiation. We consider the interactions of genes in several biological cells located on a 1-dimensional infinite grid, and we assume that the expression levels of genes are discrete. We show that the existence of a positive circuit is a necessary condition for a specific form of multistationnarity, which naturally corresponds to spatial differentiation.

• Type: Journal
• Year: 2008
• Where: ENTCS
• Authors: Anne Crumière, Paul Ruet
• Keywords: Biologist R, ENTCS 2008, Positive Circuit, Single Cell