Modelling Gene Regulatory Networks

  • Erol Gelenbe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5151)


We consider methods to compute analytical solutions for the probabilities of activation in gene regulatory networks with positive and negative feedback loops, similar to those introduced by René Thomas, and show how discrete state-space and continuous time probability models called can be used to compute their steady-state behaviour. The inclusion of logical dependencies in stochastic regulatory networks is the developed in detail.


Gene regulatory networks G-networks Stochastic models Equilibrium solutions 


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  1. 1.
    Thomas, R.: Boolean formalisation of genetic control circuits. J. Theor. Biol. 42, 565–583 (1973)CrossRefGoogle Scholar
  2. 2.
    Thomas, R., Gathoye, A.M., Lambert, L.: A complex control circuit: regulation of immunity in temperate bacteriophages. Eur. J. Biochem. 71, 211–227 (1976)CrossRefGoogle Scholar
  3. 3.
    Thomas Thomas, R.: On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. Springer Series in Synergetics, vol. 9, pp. 180–193 (1981)Google Scholar
  4. 4.
    Thomas, R.: Logical description, analysis and synthesis of biological and other networks comprising feedback loops. Adv. Chem. Phys. 55, 247–282 (1983)Google Scholar
  5. 5.
    Kaufman, M., Andris, F., Leo, O.: A Logical Analysis of T Cell Activation and Anergy. Proc. Natl. Acad. Sci. USA 96, 3894–3899 (1999)CrossRefGoogle Scholar
  6. 6.
    Thomas, R., Kaufman, M.: Multistationarity, the Basis of Cell Differentiation and Memory. I. Structural Conditions of Multistationarity and Other Non-Trivial Behaviour, and II. Logical Analysis of Regulatory Networks in Terms of Feedback Circuits, Chaos 11, 170–195 (2001)zbMATHGoogle Scholar
  7. 7.
    Gelenbe, E.: Queueing networks with negative and positive customers. Journal of Applied Probability 28, 656–663 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gelenbe, E.: G-networks with instantaneous customer movement. Journal of Applied Probability 30(3), 742–748 (1993)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Gelenbe, E.: G-Networks with signals and batch removal. Probability in the Engineering and Informational Sciences 7, 335–342 (1993)CrossRefGoogle Scholar
  10. 10.
    Fourneau, J.M., Gelenbe, E., Suros, R.: G-networks with multiple classes of positive and negative customers. Theoretical Computer Science 155, 141–156 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gelenbe, E., Fourneau, J.M.: G-Networks with resets. Performance Evaluation 49, 179–191 (2002)CrossRefzbMATHGoogle Scholar
  12. 12.
    Fourneau, J.M., Gelenbe, E.: Flow equivalence and stochastic equivalence in G-Networks. Computational Management Science 1(2), 179–192 (2004)CrossRefzbMATHGoogle Scholar
  13. 13.
    Gelenbe, E.: Learning in the recurrent random neural network. Neural Computation 5(1), 154–164 (1993)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Gelenbe, E., Pujolle, G.: Introduction to Networks of Queues, 2nd edn. J. Wiley & Sons, Chichester (1998)zbMATHGoogle Scholar
  15. 15.
    Bernot, G., Comet, J.-P., Richard, A., Guespin, J.: Application of formal methods to biological regulatory methods: extending Thomas’ asynchronous logical approach with temporal logic. J. Theoretical Biology 229(3), 339–347 (2004)CrossRefGoogle Scholar
  16. 16.
    Bernot, G., Guespin-Michel, J., Comet, J.-P., Amar, P., Zemirline, A., Delaplace, F., Ballet, P., Richard, A.: Modeling, observability and experiment: a case study. In: Proc. Dieppe School on Modeling and Simulation of Biological Processes in the Context of Genomics, pp. 49–55. Frontier Group Pub. (2003) ISBN: 2-84704-036Google Scholar
  17. 17.
    de Jong, H., Geiselmann, J., Hernandez, C., Page, M.: Genetic analyzer: qualitative simulation of genetic regulatory networks. Bioinformatics 19(3), 336–344 (2003)CrossRefGoogle Scholar
  18. 18.
    Comet, J.-P.: De la bio-informatique textuelle à une approche formelle de la biologie des systèmes, Habilitation Thesis (Thèse d’Habilitation à diriger des Recherches), Université d’Evry-Val-d’Essonne, France, November 21 (2006)Google Scholar
  19. 19.
    Gelenbe, E.: Steady-state solution of probabilistic gene regulatory networks. Physical Review E 76(1), 031903 (2007); Virtual Journal of Biological Physics Research (September 15, 2007)Google Scholar
  20. 20.
    Gelenbe, E.: Network of interacting synthetic molecules in equilibrium. Proc. Royal Society A (Mathematical and Physical Sciences) (accepted for publication)Google Scholar
  21. 21.
    Gelenbe, E., Timotheou, S.: Synchronized interactions in spiked random networks. The Computer Journal (accepted for publication)Google Scholar
  22. 22.
    Gelenbe, E.: Network of interacting synthetic molecules in equilibrium. Proc. Royal Society A (Mathematical and Physical Sciences) (accepted for publication)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Erol Gelenbe
    • 1
  1. 1.Intelligent Systems and Networks Group Department of Electrical and Electronic Engineering DepartmentImperial CollegeLondonUK

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