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On Proving the Absence of Oscillations in Models of Genetic Circuits

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Algebraic Biology (AB 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4545))

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Abstract

Using computer algebra methods to prove that a gene regulatory network cannot oscillate appears to be easier than expected. We illustrate this claim with a family of models related to historical examples.

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References

  1. Morant, P.E., Vandermoere, C., Parent, B., Lemaire, F., Corellou, F., Schwartz, C., Bouget, F.Y., Lefranc, M.: Oscillateurs génétiques simples. Applications à l’horloge circadienne d’une algue unicellulaire. In: Proceedings of the Rencontre du non linéaire, Paris (2007), http://nonlineaire.univ-lille1.fr

  2. McClung, C.R.: Plant Circadian Rhythms. The Plant Cell 18, 792–803 (2006)

    Article  Google Scholar 

  3. Fall, C.P., Marland, E.S., Wagner, J.M., Tyson, J.J. (eds.): Computational Cell Biology. Interdisciplinary Applied Mathematics, vol. 20. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  4. Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  5. Françoise, J.P.: Oscillations en biologie. Mathématiques et Applications, vol. 46. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  6. Hale, J.K., Koçak, H.: Dynamics and Bifurcations. Texts in Applied Mathematics, vol. 3. Springer, New York (1991)

    MATH  Google Scholar 

  7. Hairer, E., Norsett, S.P., Wanner, G.: Solving ordinary differential equations I. Nonstiff problems, 2nd edn. Springer Series in Computational Mathematics, vol. 8. Springer, New York (1993)

    MATH  Google Scholar 

  8. Doedel, E.: AUTO software for continuation and bifurcation problems in ODEs (1996), http://indy.cs.concordia.ca/auto

  9. Ermentrout, B.: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. Software, Environments, and Tools, vol. 14, SIAM (2002)

    Google Scholar 

  10. El Kahoui, M., Weber, A.: Deciding Hopf bifurcations by quantifier elimination in a software–component architecture. Journal of Symbolic Computation 30(2), 161–179 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Wang, D., Xia, B.: Stability Analysis of Biological Systems with Real Solution Classification. In: proceedings of ISSAC 2005, Beijing, China 354–361 (2005)

    Google Scholar 

  12. Gatermann, K., Hosten, S.: Computational algebra for bifurcation theory. Journal of Symbolic Computation 40, 1180–1207 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gatermann, K., Eiswirth, M., Sensse, A.: Toric Ideals and graph theory to analyze Hopf bifurcations in mass action systems. Journal of Symbolic Computation 40, 1361–1382 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Brown, C.W.: QEPCAD B: a program for computing with semi-algebraic sets using CADs. SIGSAM Bulletin 37(4), 97–108 (2003)

    Article  MATH  Google Scholar 

  15. Dolzmann, A., Sturm, T.: Redlog: computer algebra meets computer logic. SIGSAM Bulletin 31(2), 2–9 (1997)

    Article  MathSciNet  Google Scholar 

  16. El Din, M.S.: RAGLib (Real Algebraic Library Maple package) (2003), http://www-calfor.lip6.fr/~safey/RAGLib

  17. Goodwin, B.C.: Temporal Organization in Cells. Academic Press, London (1963)

    Google Scholar 

  18. Goodwin, B.C.: In: Advances in Enzyme Regulation, vol. 3, p. 425. Pergamon Press, Oxford (1965)

    Google Scholar 

  19. Griffith, J.S.: Mathematics of Cellular Control Processes. I. Negative Feedback to One Gene. Journal of Theoretical Biology 20, 202–208 (1968)

    Article  Google Scholar 

  20. Selleck, W., Howley, R., Fang, Q., Podolny, V., Fried, M.G., Buratowski, S., Tan, S.: A histone fold TAF octamer within the yeast TFIID transcriptional coactivator. Nature Structural Biology 8(8), 695–700 (2001)

    Article  Google Scholar 

  21. Ruoff, P., Rensing, L.: The Temperature–Compensated Goodwin Model Simulates Many Circadian Clock Properties. Journal of Theoretical Biology 179, 275–285 (1996)

    Article  Google Scholar 

  22. Ruoff, P., Vinsjevik, M., Mohsenzadeh, S., Rensing, L.: The Goodwin Model: Simulating the Effet of Cycloheximide and Heat Shock on the Sporulation Rhythm of Neurospora crassa. Journal of Theoretical Biology 196, 483–494 (1999)

    Article  Google Scholar 

  23. Kurosawa, G., Mochizuki, A., Iwasa, Y.: Comparative Study of Circadian Clock Models, in Search of Processes Promoting Oscillation. Journal of Theoretical Biology 216, 193–208 (2002)

    Article  MathSciNet  Google Scholar 

  24. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties and Algorithms. An introduction to computational algebraic geometry and commutative algebra. Undergraduate Texts in Mathematics. Springer, New York (1992)

    MATH  Google Scholar 

  25. Becker, T., Weispfenning, V.: Gröbner Bases: a computational approach to commutative algebra. Graduate Texts in Mathematics, vol. 141. Springer, Heidelberg (1991)

    Google Scholar 

  26. Basu, S., Pollack, R., Roy, M.F.: Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics, vol. 10. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  27. Collins, G.E., Akritas, A.G.: Polynomial real root isolation using Descartes’rule of signs. In: proceedings of ISSAC 1976, Yorktown Heights, NY, pp. 272–275 (1976)

    Google Scholar 

  28. Collins, G.E.: Quantifier Elimination for the Elementary Theory of Real Closed Fields by Cylindrical Algebraic Decomposition. In: Brakhage, H. (ed.) Automata Theory and Formal Languages. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)

    Google Scholar 

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Authors and Affiliations

  1. University Lille I, LIFL, 59655 Villeneuve d’Ascq, France

    François Boulier, François Lemaire & Aslı Ürgüplü

  2. University Lille I, PHLAM, 59655 Villeneuve d’Ascq, France

    Marc Lefranc & Pierre-Emmanuel Morant

Authors
  1. François Boulier
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  2. Marc Lefranc
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  3. François Lemaire
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  4. Pierre-Emmanuel Morant
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  5. Aslı Ürgüplü
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Editor information

Hirokazu Anai Katsuhisa Horimoto Temur Kutsia

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Boulier, F., Lefranc, M., Lemaire, F., Morant, PE., Ürgüplü, A. (2007). On Proving the Absence of Oscillations in Models of Genetic Circuits. In: Anai, H., Horimoto, K., Kutsia, T. (eds) Algebraic Biology. AB 2007. Lecture Notes in Computer Science, vol 4545. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73433-8_6

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  • DOI: https://doi.org/10.1007/978-3-540-73433-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73432-1

  • Online ISBN: 978-3-540-73433-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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