Distribution of essential interactions in model gene regulatory networks under mutation-selection balance

Z. Burda 1, A. Krzywicki 2, O. C. Martin 3, 4, M. Zagorski 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 82 (2010) 011908

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these degree distributions? Starting with an accepted framework of the binding of transcription factors to DNA, we consider a simple model of gene regulatory dynamics. There, we show that selection for a target expression pattern leads to the emergence of minimum connectivities compatible with the selective constraint. As a consequence, these gene networks have low in-degree, and 'functionality' is parsimonious, i.e. is concentrated on a sparse number of interactions as measured for instance by their essentiality. Furthermore, we find that mutations of the transcription factors drive the networks to have broad out-degrees. Finally, these classes of models are evolvable, i.e. significantly different genotypes can emerge gradually under mutation-selection balance.

  • 1. Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center,
    Jagellonian University
  • 2. Laboratoire de Physique Théorique d'Orsay (LPT),
    CNRS : UMR8627 – Université Paris XI - Paris Sud
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 4. Génétique Végétale (GV),
    CNRS : UMR8120 – Institut national de la recherche agronomique (INRA) : UMR0320 – Université Paris XI - Paris Sud – Institut National Agronomique Paris-Grignon