Steady state detection of chemical reaction networks using a simplified analytical method

PLoS ONE

Volumn 5, Issue 6, 2010, Pages

  Martínez Forero, Ivan ^a   Peláez López, Antonio ^a   Villoslada, Pablo ^b  

^a UNIVERSITY OF NAVARRA   (Spain)

^b INSTITUT D INVESTIGACIONS BIOMÈDIQUES AUGUST PI I SUNYER IDIBAPS   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; APOPTOSIS; ARTICLE; ARTIFICIAL NEURAL NETWORK; CHEMICAL REACTION; ENZYME DEGRADATION; GEOMETRY; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; STOICHIOMETRY; CHEMISTRY; THEORETICAL MODEL;

APOPTOSIS; CHEMISTRY; MODELS, THEORETICAL;

EID: 77956195976     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0010823     Document Type: Article

References (26)

1. Edelstein BB (1970) Biochemical model with multiple steady states and hysteresis. J Theor Biol 29: 57-62.
2. Feinberg M (1979) Lectures on Chemical Reaction Networks. Notes of lectures given at the mathematics research centre. Technical report, University of Wisconsin
3. Gatermann K, Eiswirth M, Sensse A (2005) Toric ideals and graph theory to analyze hopf bifurcations in mass action systems. Journal of Symbolic Computation 40: 1361-1382.
4. Bailey JE (2001) Complex biology with no parameters. Nat Biotechnol 19: 503-504.
5. Clarke BL (1980) Stability of complex reaction networks. Advances In Chemical Physics 43: 1-215.
6. Clarke BL (1988) Stoichiometric network analysis. Cell Biophys 12: 237-253.
7. Craciun G, Feinberg M (2006) Multiple equilibria in complex chemical reaction networks: extensions to entrapped species models. Syst Biol (Stevenage) 153: 179-186.
8. Craciun G, Tang Y, Feinberg M (2006) Understanding bistability in complex enzyme-driven reaction networks. Proc Natl Acad Sci U S A 103: 8697-8702.
9. Craciun G, Feinberg M (2005) Multiple equilibria in complex chemical reaction networks: I. the injectivity property. SIAM Journal on Applied Mathematics 65: 1526-1546.
10. Craciun G, Feinberg M (2006) Multiple equilibria in complex chemical reaction networks: II. the species-reaction graph. SIAM Journal on Applied Mathematics 66: 1321-1338.
11. Conradi C, Saez-Rodriguez J, Gilles ED, Raisch J (2005) Using chemical reaction network theory to discard a kinetic mechanism hypothesis. Syst Biol (Stevenage) 152: 243-248.
12. Shinar G, Feinberg M (2010) Structural sources of robustness in biochemical reaction networks. Science 327: 1389-1391.
13. Wee KB, Aguda BD (2006) Akt versus p53 in a network of oncogenes and tumor suppressor genes regulating cell survival and death. Biophys J 91: 857-865.
14. Bagci EZ, Vodovotz Y, Billiar TR, Ermentrout GB, Bahar I (2006) Bistability in apoptosis: roles of bax, bcl-2, and mitochondrial permeability transition pores. Biophys J 90: 1546-1559.
15. Lavrik IN, Golks A, Riess D, Bentele M, Eils R, et al. (2007) Analysis of cd95 threshold signaling: triggering of cd95 (fas/apo-1) at low concentrations primarily results in survival signaling. J Biol Chem 282: 13664-13671.
16. Hotchkiss RS, Strasser A, McDunn JE, Swanson PE (2009) Cell death. N Engl J Med 361: 1570-1583.
17. Green DR (2005) Apoptotic pathways: Ten minutes to dead. Cell 121: 671-674.
18. Albeck JG, Burke JM, Spencer SL, Lauffenburger DA, Sorger PK (2008) Modeling a snap-action, variable-delay switch controlling extrinsic cell death. PLoS Biol 6: 2831-2852.
19. Thomson M, Gunawardena J (2009) The rational parameterization theorem for multisite post-translational modification systems. J Theor Biol 261: 626-636.
20. Craciun G, Dickenstein A, Shiu A, Sturmfels B (2009) Toric dynamical systems. Journal of Symbolic Computation 44: 1551-1565.
21. Conradi C, Flockerzi D, Raisch J, Stelling J (2007) Subnetwork analysis reveals dynamic features of complex (bio)chemical networks. Proc Natl Acad Sci U S A 104: 19175-19180.
22. Conradi C, Flockerzi D, Raisch J (2008) Multistationarity in the activation of a mapk: parametrizing the relevant region in parameter space. Math Biosci 211: 105-131.
23. Sabouri-Ghomi M, Ciliberto A, Kar S, Novak B, Tyson JJ (2008) Antagonism and bistability in protein interaction networks. J Theor Biol 250: 209-218.
24. Manrai AK, Gunawardena J (2008) The geometry of multisite phosphorylation. Biophys J 95: 5533-5543.
25. Thomson M, Gunawardena J (2009) Unlimited multistability in multisite phosphorylation systems. Nature 460: 274-277.
26. Cox D, Little J, O'Shea D (2007) Ideals, varieties and algorithms Springer, third edition