Positive circuits and d-dimensional spatial differentiation: application to the formation of sense organs in Drosophila

Biosystems. 2008 Oct-Nov;94(1-2):102-8. doi: 10.1016/j.biosystems.2008.05.037. Epub 2008 Aug 3.

Abstract

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.

Publication types

  • Comparative Study

MeSH terms

  • Animals
  • Cell Differentiation*
  • Computer Simulation
  • Drosophila / genetics*
  • Drosophila / physiology
  • Gene Expression Regulation / genetics*
  • Gene Regulatory Networks / genetics*
  • Models, Genetic*
  • Sense Organs / embryology*