MABSys: Modeling and Analysis of Biological Systems

  • François Lemaire
  • Asli Ürgüplü
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6479)


We present the MABSys package which gathers, as much as possible, some functions to carry out the modeling of biochemical reaction networks, their qualitative analysis and the exact simplification of systems of ordinary differential equations. The main functions are illustrated with examples including the corresponding commands. Then we discuss Tyson’s negative feedback oscillator model and the parameters values for which this system oscillates.


software design systems of ordinary differential equations qualitative analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Boulier, F., Lefranc, M., Lemaire, F., Morant, P.-E.: Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds.) AB 2008. LNCS, vol. 5147, pp. 56–64. Springer, Heidelberg (2008), CrossRefGoogle Scholar
  2. 2.
    Boulier, F.: Réécriture algébrique dans les systèmes d’équations différentielles polynomiales en vue d’applications dans les Sciences du Vivant. H497. Université de Lille 1, LIFL, 59655 Villeneve d’Ascq France, Mémoire d’Habilitation à Diriger des Recherches (May 2006)Google Scholar
  3. 3.
    Boulier, F.: Differential Elimination and Biological Modelling. In: Rosenkranz, M., Wang, D. (eds.) Gröbner Bases in Symbolic Analysis Workshop D2.2 of the Special Semester on Gröbner Bases and Related Methods, Hagenberg Autriche. Radon Series Comp. Appl. Math, vol. 2, pp. 111–139. De Gruyter (2007)Google Scholar
  4. 4.
    Boulier, F., Lefranc, M., Lemaire, F., Morant, P.-E.: Model Reduction of Chemical Reaction Systems using Elimination. In: MACIS (2007),
  5. 5.
    Boulier, F., Lefranc, M., Lemaire, F., Morant, P.-E., Ürgüplü, A.: On Proving the Absence of Oscillations in Models of Genetic Circuits. In: Anai, H., Horimoto, K., Kutsia, T. (eds.) AB 2007. LNCS, vol. 4545, pp. 66–80. Springer, Heidelberg (2007), CrossRefGoogle Scholar
  6. 6.
    Briggs, G.E., Haldane, J.B.S.: A note on the kinetics of enzyme action. Biochemical Journal 19, 338–339 (1925)CrossRefGoogle Scholar
  7. 7.
    Griffith, J.S.: Mathematics of Cellular Control Processes. I. Negative Feedback to One Gene. Journal of Theoretical Biology 20, 202–208 (1968)CrossRefGoogle Scholar
  8. 8.
    Guckenheimer, J., Myers, M., Sturmfels, B.: Computing Hopf Bifurcations I. SIAM Journal on Numerical Analysis (1997)Google Scholar
  9. 9.
    Hairer, E., Norsett, S.P., Wanner, G.: Solving ordinary differential equations I: nonstiff problems, 2nd revised edn. Springer-Verlag New York, Inc., New York (1993)zbMATHGoogle Scholar
  10. 10.
    Hale, J., Koçak, H.: Dynamics and Bifurcations. Texts in Applied Mathematics, vol. 3. Springer, New York (1991)zbMATHGoogle Scholar
  11. 11.
    Heck, A.: Introduction to Maple, 3rd edn. Springer, Heidelberg (2003) ISBN 0-387-00230-8CrossRefzbMATHGoogle Scholar
  12. 12.
    Henri, V.: Lois générales de l’Action des Diastases. Hermann, Paris (1903)Google Scholar
  13. 13.
    Hubert, É.: AIDA Maple package: Algebraic Invariants and their Differential Algebras (2007)Google Scholar
  14. 14.
    Hubert, É., Sedoglavic, A.: Polynomial Time Nondimensionalisation of Ordinary Differential Equations via their Lie Point Symmetries. Internal Report (2006)Google Scholar
  15. 15.
    Hucka, M., Keating, S.M., Shapiro, B.E., Jouraku, A., Tadeo, L.: SBML (The Systems Biology Markup Language) (2003),
  16. 16.
    Khanin, R.: Dimensional Analysis in Computer Algebra. In: Mourrain, B. (ed.) Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, London, Ontario, Canada, July 22-25, pp. 201–208. ACM, ACM press (2001)Google Scholar
  17. 17.
    Kholodenko, B.N.: Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. European Journal of Biochemistry 267, 1583–1588 (2000)CrossRefGoogle Scholar
  18. 18.
    Lemaire, F., Maza, M.M., Xie, Y.: The RegularChains library in MAPLE 10. In: Kotsireas, I.S. (ed.) The MAPLE Conference, pp. 355–368 (2005)Google Scholar
  19. 19.
    Lemaire, F., Ürgüplü, A.: A Method for Semi-Rectifying Algebraic and Differential Systems using Scaling type Lie Point Symmetries with Linear Algebra. In: Proceedings of ISSAC (2010) (to appear)Google Scholar
  20. 20.
    Lemaire, F., Ürgüplü, A.: Modeling and Analysis of Biological Systems. Maple Package (2008),
  21. 21.
    Mansfield, E.: Indiff: a MAPLE package for over determined differential systems with Lie symmetry (2001)Google Scholar
  22. 22.
    Michaëlis, L., Menten, M.: Die Kinetik der Invertinwirkung (the kinetics of invertase activity). Biochemische Zeitschrift 49, 333–369 (1973), Partial english translation,
  23. 23.
    Murray, J.D.: Mathematical Biology. Interdisciplinary Applied Mathematics, vol. 17. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  24. 24.
    Okino, M.S., Mavrovouniotis, M.L.: Simplification of Mathematical Models of Chemical Reaction Systems. Chemical Reviews 98(2), 391–408 (1998)CrossRefGoogle Scholar
  25. 25.
    Ritt, J.F.: Differential Algebra. American Mathematical Society Colloquium Publications, vol. XXXIII. AMS, New York (1950), Google Scholar
  26. 26.
    Sedoglavic, A.: Reduction of Algebraic Parametric Systems by Rectification of Their Affine Expanded Lie Symmetries. In: Anai, H., Horimoto, K., Kutsia, T. (eds.) AB 2007. LNCS, vol. 4545, pp. 277–291. Springer, Heidelberg (2007), CrossRefGoogle Scholar
  27. 27.
    Sedoglavic, A., Ürgüplü, A.: Expanded Lie Point Symmetry, Maple package (2007),
  28. 28.
    Smolen, P., Baxter, D.A., Byrne, J.H.: Modeling circadian oscillations with interlocking positive and negative feedback loops. Journal of Neuroscience 21, 6644–6656 (2001)Google Scholar
  29. 29.
    Szallasi, Z., Stelling, J., Periwal, V. (eds.): System Modeling in Cellular Biology. The MIT Press, Cambridge (2006)Google Scholar
  30. 30.
    Tyson, J.J., Chen, K.C., Novak, B.: Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Current Opinion in Cell Biology 15, 221–231 (2003)CrossRefGoogle Scholar
  31. 31.
    Ürgüplü, A.: Contribution to Symbolic Effective Qualitative Analysis of Dynamical Systems; Application to Biochemical Reaction Networks. PhD thesis, University of Lille 1 (January 13, 2010)Google Scholar
  32. 32.
    Vora, N., Daoutidis, P.: Nonlinear model reduction of chemical reaction systems. AIChE (American Institute of Chemical Engineers) Journal 47(10), 2320–2332 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • François Lemaire
    • 1
  • Asli Ürgüplü
    • 1
  1. 1.University of Lille I, LIFLVilleneuve d’AscqFrance

Personalised recommendations