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Spatial differentiation and positive circuits in a discrete framework

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Crumière, Anne | Ruet, Paul

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International audience. 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 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.

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