Bulletin of Mathematical Biology

, Volume 71, Issue 6, pp 1394–1431

Stochastic Models and Numerical Algorithms for a Class of Regulatory Gene Networks

  • Thomas Fournier
  • Jean-Pierre Gabriel
  • Christian Mazza
  • Jerôme Pasquier
  • José Galbete
  • Nicolas Mermod
Original Article

DOI: 10.1007/s11538-009-9407-9

Cite this article as:
Fournier, T., Gabriel, JP., Mazza, C. et al. Bull. Math. Biol. (2009) 71: 1394. doi:10.1007/s11538-009-9407-9

Abstract

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856–860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Keywords

Gillespie algorithmGene networkSelf-promoterQuasi-equilibriumDimerizationMean fieldTime delay

Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  • Thomas Fournier
    • 1
  • Jean-Pierre Gabriel
    • 1
  • Christian Mazza
    • 1
  • Jerôme Pasquier
    • 1
  • José Galbete
    • 2
  • Nicolas Mermod
    • 2
  1. 1.Department of MathematicsUniversity of FribourgFribourgSwitzerland
  2. 2.Institute of BiotechnologyUniversity of LausanneLausanneSwitzerland