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Communication Dans Un Congrès Année : 2008

Spatial differentiation and positive circuits in a discrete framework

Résumé

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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Dates et versions

hal-00692089 , version 1 (28-04-2012)

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Anne Crumière, Paul Ruet. Spatial differentiation and positive circuits in a discrete framework. Development of Computational Models, 2007, Poland. pp.85-100, ⟨10.1016/j.entcs.2008.10.029⟩. ⟨hal-00692089⟩
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