Skip to main content

Piecewise-Linear Models of Genetic Regulatory Networks: Theory and Example

  • Chapter
Biology and Control Theory: Current Challenges

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 357))

Abstract

The experimental study of genetic regulatory networks has made tremendous progress in recent years resulting in a huge amount of data on the molecular interactions in model organisms. It is therefore not possible anymore to intuitively understand how the genes and interactions together influence the behavior of the system. In order to answer such questions, a rigorous modeling and analysis approach is necessary. In this chapter, we present a family of such models and analysis methods enabling us to better understand the dynamics of genetic regulatory networks. We apply such methods to the network that underlies the nutritional stress response of the bacterium E. coli.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Botsford and J. Harman. Cyclic AMP in prokaryotes. Microbiological reviews, 56(1):100–122, 1992.

    Google Scholar 

  2. K. Bouraima Madjebi. Etude de modèles de réseau de régulation génique. Master’s thesis, University of Orsay, 2005.

    Google Scholar 

  3. R. Casey, H. de Jong, and J.-L. Gouzé. Piecewise-linear models of genetic regulatory networks: Equilibria and their stability. J. Math. Biol., 52:27–56, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. Cristescu. Algorithmic study on genetic regulatory networks. Technical report, Automatic control and computer science faculty, Politechnica University of Bucharest, 2006. internship report.

    Google Scholar 

  5. H. de Jong. Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol., 9:67–103, 2002.

    Article  Google Scholar 

  6. H. de Jong, J. Geiselmann, C. Hernandez, and M. Page. Genetic Network Analyzer: Qualitative simulation of genetic regulatory networks. Bioinformatics, 19(3):336–344, 2003.

    Article  Google Scholar 

  7. H. de Jong, J.-L. Gouzé, C. Hernandez, M. Page, T. Sari, and J. Geiselmann. Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull. Math. Biol., 6:301–340, 2004.

    Google Scholar 

  8. E. Farcot and J.-L. Gouzé. How to control a biological switch: a mathematical framework for the control of piecewise affine models of gene networks. Research Report 5979, INRIA, 09 2006.

    Google Scholar 

  9. E. Farcot and J.-L. Gouzé. Periodic solutions of piecewise affine gene network models: the case of a negative feedback loop. Research Report 6018, INRIA, 11 2006.

    Google Scholar 

  10. A._F. Filippov. Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht, 1988.

    Google Scholar 

  11. R. Ghosh and C. Tomlin. Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. Systems Biology, 1(1):170–183, 2004.

    Article  Google Scholar 

  12. L. Glass and S. Kauffman. The logical analysis of continuous non-linear biochemical control networks. J. Theor. Biol., 39:103–129, 1973.

    Article  Google Scholar 

  13. J. Gouzé and T. Sari. A class of piecewise linear differential equations arising in biological models. Dyn. Syst, 17:299–316, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  14. L. Habets and J. van Schuppen. A control problem for affine dynamical systems on a full-dimensional polytope. Automatica, 40:21–35, 2004.

    Article  MATH  Google Scholar 

  15. H._M. Hardin and J. van Schuppen. System reduction of nonlinear positive systems by linearization and truncation. In C. Commault and N. Marchand, editors, Positive systems-Proceedings of the Second Multidisciplinary Symposium on Positive Systems: Theory and Applications (POSTA 06), volume 341 of Lecture Notes in Control and Information Sciences, pages 431–438. Grenoble, France, 2006.

    Google Scholar 

  16. J. Harman. Allosteric regulation of the cAMP receptor protein. Biochimica et Biophysica Acta, 1547(1):1–17, 2001.

    Google Scholar 

  17. K. Heidtke and S. Schulze-Kremer. Design and implementation of a qualitative simulation model of λ phage infection. Bioinformatics, 14(1):81–91, 1998.

    Article  Google Scholar 

  18. R. Hengge-Aronis. The general stress response in Escherichia coli. InG. Storz and R. Hengge-Aronis, editors, Bacterial Stress Responses, pages 161–177. ASM Press, Washington, DC, 2000.

    Google Scholar 

  19. G. Huisman, D. Siegele, M. Zambrano, and R. Kolter. Morphological and physiological changes during stationary phase. In F. Neidhardt, R. Curtiss III, J. Ingraham, E. Lin, K. Low, B. Magasanik, W. Reznikoff, M. Riley, M. Schaechter, and H. Umbarger, editors, Escherichia coli and Salmonella: Cellular and Molecular Biology, pages 1672–1682. ASM Press, Washington, DC, 2nd edition, 1996.

    Google Scholar 

  20. S. Kauffman. The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, New York, 1993.

    Google Scholar 

  21. A. Keil and J.-L. Gouzé. Model reduction of modular systems using balancing methods. Technical report, Munich University of Technology, 2003.

    Google Scholar 

  22. I. Koch, B. Junker, and M. Heiner. Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics, 2005. In press.

    Google Scholar 

  23. K. Kohn. Molecular interaction maps as information organizers and simulation guides. Chaos, 11(1):84–97, 2001.

    Article  MATH  Google Scholar 

  24. A. Martinez-Antonio and J. Collado-Vides. Identifying global regulators in transcriptional regulatory networks in bacteria. Current Opinion in Microbiology, 6(5):482–489, 2003.

    Article  Google Scholar 

  25. T. Mestl, E. Plahte, and S. Omholt. A mathematical framework for describing and analysing gene regulatory networks. Journal of Theoretical Biology, 176(2):291–300, 1995.

    Article  MathSciNet  Google Scholar 

  26. M. Ptashne. A Genetic Switch: Phage λ and Higher Organisms. Cell Press & Blackwell Science, Cambridge, MA, 2nd edition, 1992.

    Google Scholar 

  27. V. Reddy, M. Liebman, and M. Mavrovouniotis. Qualitative analysis of biochemical reaction systems. Computers in Biology and Medicine, 26(1):9–24, 1996.

    Article  Google Scholar 

  28. A. Regev, W. Silverman, and E. Shapiro. Representation and simulation of biochemical processes using the π-calculus process algebra. In R. Altman, A. Dunker, L. Hunter, K. Lauderdale, and T. Klein, editors, Pacific Symposium on Biocomputing, PSB’01, volume 6, pages 459–470, Singapore, 2001. World Scientific Publishing.

    Google Scholar 

  29. D. Ropers, H. de Jong, M. Page, D. Schneider, and J. Geiselmann. Qualitative simulation of the carbon starvation response in Escherichia coli. BioSystems, 84:124–152, 2006.

    Article  Google Scholar 

  30. R. Thomas and R. d’Ari. Biological Feedback. CRC Press, Boca Raton, FL, 1990.

    MATH  Google Scholar 

  31. J. Wang, E. Gilles, J. Lengeler, and K. Jahreis. Modeling of inducer exclusion and catabolite repression based on a PTS-dependent sucrose and non-PTS-dependent glycerol transport systems in Escherichia coli K-12 and its experimental verification. Journal of Biotechnology, 92(2):133–158, 2001.

    Article  Google Scholar 

  32. L. Wick and T. Egli. Molecular components of physiological stress responses in Escherichia coli. Advances in Biochemical Engineering/Biotechnology, 89:1–45, 2004.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Grognard, F., de Jong, H., Gouzé, JL. (2007). Piecewise-Linear Models of Genetic Regulatory Networks: Theory and Example. In: Queinnec, I., Tarbouriech, S., Garcia, G., Niculescu, SI. (eds) Biology and Control Theory: Current Challenges. Lecture Notes in Control and Information Sciences, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71988-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71988-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71987-8

  • Online ISBN: 978-3-540-71988-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics