Algorithm for identification of piecewise smooth hybrid systems: Application to eukaryotic cell cycle regulation

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

Volumn 6833 LNBI, Issue , 2011, Pages 225-236

  Noel, Vincent ^a,b   Vakulenko, Sergei ^d   Radulescu, Ovidiu ^b,c  

^a UNIVERSITÉ DE RENNES 1   (France)

^b UNIVERSITÉ DE MONTPELLIER   (France)

^c INRIA   (France)

^d Department of APO   (Russian Federation)

Author keywords

cell cycle; hybrid models; systems biology

Indexed keywords

CELLS; HYBRID SYSTEMS; MOLECULAR BIOLOGY;

CELL CYCLE; DISSIPATIVE SYSTEMS; EUKARYOTIC CELL CYCLE; HYBRID MODEL; PIECEWISE SMOOTH MODELS; REGULATORY NETWORK; SYSTEMS BIOLOGY; TOP DOWN APPROACHES;

BIOLOGICAL SYSTEMS;

EID: 80052998883     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-23038-7_20     Document Type: Conference Paper

References (20)

1. Barton, P.I., Banga, J.R., Galan, S.: Optimization of hybrid discrete/continuous dynamic systems. Computers & Chemical Engineering 24(9-10), 2171-2182 (2000)
2. Chu, K.W., Deng, Y., Reinitz, J.: Parallel simulated annealing by mixing of states 1. Journal of Computational Physics 148(2), 646-662 (1999)
3. Csikász-Nagy, A., Battogtokh, D., Chen, K.C., Novák, B., Tyson, J.J.: Analysis of a generic model of eukaryotic cell-cycle regulation. Biophysical Journal 90(12), 4361-4379 (2006)
4. Di Bernardo, M.: Piecewise-smooth dynamical systems: theory and applications. Springer, Heidelberg (2008)
5. De Jong, H., Gouzé, J.L., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bulletin of Mathematical Biology 66(2), 301-340 (2004)
6. Dang, T., Maler, O., Testylier, R.: Accurate hybridization of nonlinear systems. In: Proceedings of the 13th ACM International Conference on Hybrid systems: Computation and Control, pp. 11-20. ACM, New York (2010)
7. Filippov, A.F., Arscott, F.M.: Differential equations with discontinuous righthand sides. Springer, Heidelberg (1988)
8. Gorban, A.N., Radulescu, O.: Dynamic and static limitation in reaction networks, revisited. In: West, D., Marin, G.B., Yablonsky, G.S. (eds.) Advances in Chemical Engineering - Mathematics in Chemical Kinetics and Engineering. Advances in Chemical Engineering, vol. 34, pp. 103-173. Elsevier, Amsterdam (2008)
9. Gebert, J., Radde, N., Weber, G.W.: Modeling gene regulatory networks with piecewise linear differential equations. European Journal of Operational Research 181(3), 1148-1165 (2007)
10. Gorban, A.N., Radulescu, O., Zinovyev, A.Y.: Asymptotology of chemical reaction networks. Chemical Engineering Science 65, 2310-2324 (2010)
11. Liebermeister, W., Uhlendorf, J., Klipp, E.: Modular rate laws for enzymatic reactions: thermodynamics, elasticities and implementation. Bioinformatics 26(12), 1528 (2010)
12. Matveev, A.S., Savkin, A.V.: Qualitative theory of hybrid dynamical systems. Birkhäuser, Basel (2000)
13. Novak, B., Tyson, J.J.: A model for restriction point control of the mammalian cell cycle. Journal of Theoretical Biology 230(4), 563-579 (2004)
14. Radulescu, O., Gorban, A.N., Zinovyev, A., Lilienbaum, A.: Robust simplifications of multiscale biochemical networks. BMC Systems Biology 2(1), 86 (2008)
15. Savageau, M.A., Voit, E.O.: Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Mathematical Biosciences 87(1), 83-115 (1987)
16. Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C.: Stability Criteria for Switched and Hybrid Systems. SIAM Review-The Flagship Journal of the Society for Industrial and Applied Mathematics 49(4), 545-592 (2007)
17. Tavernini, L.: Differential automata and their discrete simulators. Nonlinear Anal. Theory Methods Applic. 11(6), 665-683 (1987)
18. Tyson, J.J.: Modeling the cell division cycle: cdc2 and cyclin interactions. Proceedings of the National Academy of Sciences of the United States of America 88(16), 7328 (1991)
19. Vakulenko, S.: Complexité dynamique des réseaux de Hopfield: Dynamical complexity of the Hopfield networks. Comptes Rendus Mathematique 335(7), 639-642 (2002)
20. Vakulenko, S., Grigoriev, D.: Complexity of gene circuits, pfaffian functions and the morphogenesis problem. Comptes Rendus Mathematique 337(11), 721-724 (2003)