Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Thomas, R.: Boolean formalisation of genetic control circuits. J. Theor. Biol. 42, 565–583 (1973)
Thomas, R., Gathoye, A.M., Lambert, L.: A complex control circuit: regulation of immunity in temperate bacteriophages. Eur. J. Biochem. 71, 211–227 (1976)
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)
Thomas, R.: Logical description, analysis and synthesis of biological and other networks comprising feedback loops. Adv. Chem. Phys. 55, 247–282 (1983)
Kaufman, M., Andris, F., Leo, O.: A Logical Analysis of T Cell Activation and Anergy. Proc. Natl. Acad. Sci. USA 96, 3894–3899 (1999)
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)
Gelenbe, E.: Queueing networks with negative and positive customers. Journal of Applied Probability 28, 656–663 (1991)
Gelenbe, E.: G-networks with instantaneous customer movement. Journal of Applied Probability 30(3), 742–748 (1993)
Gelenbe, E.: G-Networks with signals and batch removal. Probability in the Engineering and Informational Sciences 7, 335–342 (1993)
Fourneau, J.M., Gelenbe, E., Suros, R.: G-networks with multiple classes of positive and negative customers. Theoretical Computer Science 155, 141–156 (1996)
Gelenbe, E., Fourneau, J.M.: G-Networks with resets. Performance Evaluation 49, 179–191 (2002)
Fourneau, J.M., Gelenbe, E.: Flow equivalence and stochastic equivalence in G-Networks. Computational Management Science 1(2), 179–192 (2004)
Gelenbe, E.: Learning in the recurrent random neural network. Neural Computation 5(1), 154–164 (1993)
Gelenbe, E., Pujolle, G.: Introduction to Networks of Queues, 2nd edn. J. Wiley & Sons, Chichester (1998)
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)
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: 2-84704-036
de Jong, H., Geiselmann, J., Hernandez, C., Page, M.: Genetic analyzer: qualitative simulation of genetic regulatory networks. Bioinformatics 19(3), 336–344 (2003)
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)
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)
Gelenbe, E.: Network of interacting synthetic molecules in equilibrium. Proc. Royal Society A (Mathematical and Physical Sciences) (accepted for publication)
Gelenbe, E., Timotheou, S.: Synchronized interactions in spiked random networks. The Computer Journal (accepted for publication)
Gelenbe, E.: Network of interacting synthetic molecules in equilibrium. Proc. Royal Society A (Mathematical and Physical Sciences) (accepted for publication)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gelenbe, E. (2008). Modelling Gene Regulatory Networks. In: LiĂ², P., Yoneki, E., Crowcroft, J., Verma, D.C. (eds) Bio-Inspired Computing and Communication. BIOWIRE 2007. Lecture Notes in Computer Science, vol 5151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92191-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-92191-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92190-5
Online ISBN: 978-3-540-92191-2
eBook Packages: Computer ScienceComputer Science (R0)