Open AccessSpatial Differentiation and Positive Circuits in a Discrete Framework
Author(s) -
Anne Crumière,
Paul Ruet
Publication year - 2008
Publication title -
electronic notes in theoretical computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.242
H-Index - 60
ISSN - 1571-0661
DOI - 10.1016/j.entcs.2008.10.029
Subject(s) - graph , mathematics , gene regulatory network , electronic circuit , computer science , theoretical computer science , discrete mathematics , gene , topology (electrical circuits) , combinatorics , biology , genetics , gene expression , electrical engineering , engineering
The biologist R. Thomas has enounced a rule relating multistationarity in a system of genes interacting in a single cell to the existence of a positive circuit in the regulatory graph of the system. 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 Boolean. We show that the existence of a positive circuit is a necessary condition for a specific form of multistationarity, which naturally corresponds to spatial differentiation
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