Reduction of chemical reaction networks using quasi-integrals

Journal of Physical Chemistry A

Volumn 109, Issue 3, 2005, Pages 441-450

  Straube, Ronny ^a   Flockerzi, Dietrich ^b   Müller, Stefan C ^a   Hauser, Marcus J B ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b MAX PLANCK INSTITUTE FOR DYNAMICS OF COMPLEX TECHNICAL SYSTEMS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL SPECIES; FUNCTIONAL EQUATIONS; INTRINSIC SYSTEMS; REACTION NETWORKS;

APPROXIMATION THEORY; COMPLEXATION; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PH EFFECTS; REDUCTION;

REACTION KINETICS;

HEMIN; HYDROGEN; NICOTINAMIDE ADENINE DINUCLEOTIDE; OXIDOREDUCTASE; PEROXIDASE; PEROXIDE; SULFITE;

ARTICLE; CHEMICAL MODEL; CHEMISTRY; METABOLISM; OXIDATION REDUCTION REACTION;

HEMIN; HYDROGEN; MODELS, CHEMICAL; NAD; OXIDATION-REDUCTION; OXIDOREDUCTASES; PEROXIDASE; PEROXIDES; SULFITES;

EID: 13444302621     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp045665s     Document Type: Article

References (34)

1. Michal, G. Biochemical pathways; Spectrum: Heidelberg, Germany, 1999.
2. Keener, J.; Sneyd, J. Mathematical Physiology; Springer: New York, 1998.
3. Warneck, P. Phys. Chem. Chem. Phys. 1999, 1, 5471.
4. Geiger, H.; Barnes, I.; Becker, K. H.; Bohn, B.; Brauers, T.; Donner, B.; Dorn, H.-P.; Elend, M.; Freitas Dinis, C. M.; Grossmann, D.; Hass, H.; Hein, H.; Hoffmann, A.; Hoppe, L.; Hülsemann, F.; Kley, D.; Klotz, B.; Libuda, H. G.; Maurer, T.; Mihelcic, D.; Moortgat, G. K.; Olariu, R.; Neeb, P.; Poppe, D.; Ruppert, L.; Sauer, C. G.; Shestakov, O.; Somnitz, H.; Stockwell, W. R.; Thüner, L. P.; Wahner, A.; Wiesen, P.; Zabel, F.; Zellner, R.; Zetzsch, C. J. Atmos. Chem. 2002, 42, 323.
5. Allara, D. L.; Edelson, D. Int. J. Chem. Kinet. 1975, 7, 479.
6. Warnatz, J. Pure Appl. Chem. 2000, 72, 2101.
7. Györgyi, L.; Turányi, T.; Field, R. J. J. Phys. Chem. 1990, 94, 7162.
8. Aguda, B. D.; Clarke, B. L. J. Chem. Phys. 1987, 87, 3461.
9. Eiswirth, M.; Freund, A.; Ross, J. Adv. Chem. Phys. 1991, 80, 127.
10. Hung, Y.-F.; Schreiber, I.; Ross, J. J. Chem. Phys. 1995, 99, 1980.
11. Clarke, B. L. Adv. Chem. Phys. 1980, 43, 1.
12. Turányi, T. J. Math. Chem. 1990, 5, 203.
13. Price, N. D.; Reed, J. L.; Papin, J. A.; Wiback, S. J.; Palsson, B. O. J. Theor. Biol. 2003, 225, 185.
14. Vajda, S.; Turányi, T. J. Phys. Chem. 1986, 90, 1664.
15. Fenichel, N. J. Differ. Equat. 1979, 31, 53.
16. Tichonov, A. N. Mat. Sb. 1952, 31, 575.
17. O'Malley, R. E. Singular Perturbation Methods for Ordinary Differential Equations; Springer New York, 1991; p 83.
18. Li, G.; Tomlin, A. S.; Rabitz, H.; Tóth, J. J. Chem. Phys. 1993, 99, 3562.
19. Roussel, M. R.; Fraser, S. J. Chaos 2001, 11, 196.
20. Lam, S. H. Combust. Sci. Technol. 1993, 89, 375.
21. Lin, C. C.; Segel, L. A. Mathematics Applied to Deterministic Problems in the Natural Sciences; SIAM: Philadelphia, PA, 1994.
22. Stiefenhofer, M. J. Math. Biol. 1998, 36, 593.
23. Ermentrout, B. Simulating, Analyzing and Dynamical Systems: A Guide to XPPAUT for Researchers and Students; SIAM: Philadelphia, PA, 2002. http://www.math.pitt.edu/[IMAGE]bard/xpp/xpp.html.
24. Kuznetsov, Y. Elements of Applied Bifurcation Theory; Springer: Heidelberg, Germany, 1998.
25. Hauser, M. J. B.; Strich, A.; Bakos, R.; Nagy-Ungvárai, Zs.; Müller, S. C. Faraday Discuss. 2001, 120, 229.
26. Hauser, M. J. B.; Fricke, N.; Storb, U.; Müller, S. C. Z. Phys. Chem. 2002, 216, 375.
27. Straube, R.; Müller, S. C.; Hauser, M. J. B. Z. Phys. Chem. 2003, 217, 1427.
28. Schuster, S.; Schuster, R. J. Math. Chem. 1989, 3, 25.
29. Hauser, M. J. B.; Olsen, L. F. In Transport versus Structure - Their Competitive Roles in Biophysics and Chemistry; Müller, S. C., Parisi, P., Zimmermann, W., Eds.; Springer: Heidelberg, Germany, 1999; p 252.
30. Scheeline, A.; Olson, D. L.; Williksen, E. P.; Horras, G. A.; Klein, M. L.; Larter, R. Chem. Rev. 1997, 97, 793.
31. Larter, R.; Olsen, L. F.; Steinmetz, C. G.; Geest, T. In Chaos in Chemical and Biological Systems; Field, R. J., Györgyi, L., Eds.; World Scientific: Singapore, 1993; p 175.
32. Bronnikova, T. V.; Fed'kina, V. R.; Schaffer, W. M.; Olsen, L. F. J. Phys. Chem. 1995, 99, 9309.
33. Hauser, M. J. B.; Olsen, L. F. J. Chem. Soc., Faraday Trans. 1996, 92, 2857.
34. Hauser, M. J. B.; Olsen, L. F.; Bronnikova, T. V.; Schaffer, W. M. J. Phys. Chem. B 1997, 101, 5075.