Positive circuits and d-dimensional spatial differentiation: application to the formation of sense organs in Drosophila.
We discuss a rule proposed by the biologist Thomas according to which the possibility for a genetic network (represented by a signed directed graph called a regulatory graph) to have several stable states implies the existence of a positive circuit. This result is already known for different models, differential or discrete formalism, but always with a network of genes contained in a single cell. Thus, we can ask about the validity of this rule for a system containing several cells and with intercellular genetic interactions. In this paper, we consider the genetic interactions between several cells located on a d-dimensional lattice, i.e., each point of lattice represents a cell to which we associate the expression level of n genes contained in this cell. With this configuration, 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. We then illustrate this theorem through the example of the formation of sense organs in Drosophila.
Crumière
Anne
A
Institut de Mathématiques de Luminy, Campus de Luminy, Marseille Cedex 9, France. crumiere@iml.univ-mrs.fr
Sablik
Mathieu
M
D000818:Animals; D002454:Cell Differentiation; D003198:Computer Simulation; D004330:Drosophila / Q000235:genetics* / Q000502:physiology; D005786:Gene Expression Regulation / Q000235:genetics*; D053263:Gene Regulatory Networks / Q000235:genetics*; D008957:Models, Genetic; D012679:Sense Organs / Q000196:embryology*