Chemical reaction systems, computer algebra and systems biology: (Invited talk)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6885 LNCS, Issue , 2011, Pages 73-87

  Boulier, François ^a   Lemaire, François ^a   Petitot, Michel ^a   Sedoglavic, Alexandre ^a  

^a UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BIO-COMPUTING; CHEMICAL REACTION SYSTEMS; CIRCADIAN CLOCK; COMPUTER ALGEBRA; DETERMINISTIC MODELS; EFFICIENT ALGORITHM; GREEN ALGA; INVITED TALK; JOINT PROJECTS; MODELING PROBLEMS; OSTREOCOCCUS TAURI; REDUCTION PROBLEM; STATISTICAL MOMENTS; STOCHASTIC DYNAMICS; SYSTEMS BIOLOGY; SYSTEMS OF EQUATIONS; COMPUTER ALGEBRA SOFTWARES;

ALGAE; ALGORITHMS; CHEMICAL REACTIONS; DYNAMICS; STOCHASTIC SYSTEMS;

ALGEBRA;

EID: 80052798375     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-23568-9_7     Document Type: Conference Paper

References (42)

1. Bächler, T., Gerdt, V., Lange-Hegermann, M., Robertz, D.: Thomas Decomposition of Algebraic and Differential Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2010. LNCS, vol. 6244, pp. 31-54. Springer, Heidelberg (2010)
2. Batt, G., Page, M., Cantone, I., Goessler, G., Monteiro, P., de Jong, H.: Efficient parameter search for qualitative models of regulatory networks using symbolic model checking. In: ECCB, vol. 26, pp. i603-i610 (2010)
3. Boulier, F., Lazard, D., Ollivier, F., Petitot, M.: Computing representations for radicals of finitely generated differential ideals. Applicable Algebra in Engineering, Communication and Computing 20(1), 73-121 (2009); (1997 Tech. rep. IT306 of the LIFL)
4. Boulier, F., Lefranc, M., Lemaire, F., Morant, P.-E.: Model Reduction of Chemical Reaction Systems using Elimination. Presented at the International Conference MACIS 2007 (2007), http://hal.archives-ouvertes.fr/hal-00184558
5. 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)
6. 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), http://hal.archives-ouvertes. fr/hal-00139667
7. Brown, C.W.: QEPCAD B: a program for computing with semi-algebraic sets using CADs. SIGSAM Bulletin 37(4), 97-108 (2003), http://www.cs.usna.edu/ ~qepcad/B/QEPCAD.html
8. Chaves, M., Sontag, E.D.: State-Estimators for Chemical Reaction Networks of Feinberg-Horn-Jackson Zero Deficiency Type. European Journal Control 8, 343-359 (2002)
9. The Cytoscape Consortium. Cytoscape: An Open Source Platform for Complex Network Analysis and Visualization (2001-2010), http://www.cytoscape.org
10. Dolzmann, A., Sturm, T.: Redlog: computer algebra meets computer logic. SIGSAM Bulletin 31(2), 2-9 (1997)
11. El Din, M.S.: RAGLib: A library for real solving polynomial systems of equations and inequalities (2007), http://www-salsa.lip6.fr/~safey/RAGLib
12. Derelle, É., et al.: Genome Analysis of the smallest free-living eukaryote Ostreococcus tauri unveils many unique features. Proceedings of the National Academy of Science of the USA 103(31) (August 2006)
13. Fages, F., Soliman, S., Chabrier-Rivier, N.: Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM. Journal of Biological Physics and Chemistry 4, 64-73 (2004)
14. Feinberg, M.: The Existence and Uniqueness of Steady States for a Classe of Chemical Reaction Networks. Arch. Rational Mech. Anal. 132, 311-370 (1995)
15. Gatermann, K., Eiswirth, M., Sensse, A.: Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems. Journal of Symbolic Computation 40(6), 1361-1382 (2005)
16. Gillespie, C.S.: Moment-closure approximations for mass-action models. Systems Biology, IET 3(1) (2009)
17. Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions. Journal of Physical Chemistry 81(25), 2340-2361 (1977)
18. Henri, V.: Lois générales de l'Action des Diastases. Hermann, Paris (1903)
19. Kœrn, M., Elston, T.C., Blake, W.J., Collins, J.J.: Stochasticity in gene expression: from theories to phenotypes. Nature 6, 451-464 (2005)
20. Kokotovic, P., Khalil, H.K., O'Reilly, J.: Singular Perturbation Methods in Control: Analysis and Design. Classics in Applied Mathematics, vol. 25. SIAM, Philadelphia (1999)
21. 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)
22. 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, München, Germany, pp. 85-92 (August 2010)
23. Lemaire, F., Ürgüplü, A.: Mabsys: Modeling and analysis of biological systems. In: Horimoto, K., Nakatsui, M., Popov, N. (eds.) Proceedings of Algebraic and Numeric Biology 2010, Castle of Hagenberg, Austria (August 2010)
24. Lemaire, F., Ürgüplü, A.: The MABSys MAPLE package (2010), http://www.lifl.fr/~lemaire/MABSys
25. Michaelis, L., Menten, M.: Die kinetik der invertinwirkung. Biochemische Zeitschrift 49, 333-369 (1973), Partial translation in english on http://web.lemoyne.edu/~giunta/menten.html
26. Moroz, G., Rouillier, F.: DV: Un logiciel de classification des solutions réelles d'un système paramétré (2009), http://www-spiral.lip6.fr/~moroz/fr/software.html
27. Murray, J.D.: Mathematical Biology I. An Introduction, 3rd edn. Interdisciplinary Applied Mathematics, vol. 17. Springer, Heidelberg (2002)
28. Niu, W.: Qualitative Analysis of Biological Systems Using Algebraic Methods. PhD thesis, Université Paris VI, Paris (June 2011)
29. Nöthen, A.L.: Quasistationarität und Fast-Invariante Mengen Gewönlicher Differentialgleichungen. PhD thesis, Rheinisch- Westfälischen Technischen Hochschule (2008)
30. Othmer, H.G.: Analysis of Complex Reaction Networks in Signal Transduction, Gene Control and Metabolism (2006), http://www.ricam.oeaw.ac.at/ publications/download/summerschool/LectureNotes.Othmer.pdf
31. Paulsson, J.: Models of stochastic gene expression. Physics of Life Reviews 2, 157-175 (2005)
32. Paulsson, J., Elf, J.: Stochastic Modeling of Intracellular Kinetics. In: Szallasi, Z., Stelling, J., Periwal, V. (eds.) System Modeling in Cellular Biology: From Concepts to Nuts and Bolts, pp. 149-175. The MIT Press, Cambridge (2006)
33. Érdi, P., Tóth, J.: Mathematical models of chemical reactions: theory and applications of deterministic and stochastic models. Princeton University Press, Princeton (1989)
34. Petitot, M.: The MAGNUS MAPLE software (2010), http://www.lifl.fr/ ~petitot/recherche/exposes/ANB2010
35. 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)
36. Sedoglavic, A., Ürgüplü, A.: Expanded Lie Point Symmetry, MAPLE package (2007), http://www.lifl.fr/~sedoglav/Software
37. Singh, A., Hespanha, J.P.: Lognormal Moment Closures for Biochemical Reactions. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 2063-2068 (2006)
38. Ürgüplü, A.: Contribution to Symbolic Effective Qualitative Analysis of Dynamical Systems; Application to Biochemical Reaction Networks. PhD thesis, University Lille I, Lille, France (2010)
39. Van Breusegem, V., Bastin, G.: Reduced order dynamical modelling of reaction systems: a singular perturbation approach. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, pp. 1049-1054 (December 1991)
40. Vidal, S., Petitot, M., Boulier, F., Lemaire, F., Kuttler, C.: Models of Stochastic Gene Expression and Weyl Algebra. In: Horimoto, K., Nakatsui, M., Popov, N. (eds.) Proceedings of Algebraic and Numeric Biology 2010, Castle of Hagenberg, Austria, pp. 50-67 (August 2010)
41. Vilar, J.M.G., Kueh, H.Y., Barkai, N., Leibler, S.: Mechanisms of noise-resistance in genetic oscillators. Proceedings of the National Academy of Science of the USA 99(9), 5988-5992 (2002)
42. Xia, B.: DISCOVERER: A tool for solving semi-algebraic systems. ACM Commun. Comput. Algebra 41, 102-103 (2007)