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

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 algorithm Gene network Self-promoter Quasi-equilibrium Dimerization Mean field Time delay 

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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

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