Reduction of Chemical Reaction Networks Using Quasi-Integrals
| العنوان: | Reduction of Chemical Reaction Networks Using Quasi-Integrals |
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| المؤلفون: | Marcus J. B. Hauser, Ronny Straube, Dietrich Flockerzi, Stefan C. Müller |
| المصدر: | The Journal of Physical Chemistry A. 109:441-450 |
| بيانات النشر: | American Chemical Society (ACS), 2004. |
| سنة النشر: | 2004 |
| مصطلحات موضوعية: | Singular perturbation, Dynamical systems theory, Chemistry, Numerical analysis, NAD, Peroxides, Models, Chemical, Flow (mathematics), Slow manifold, Ordinary differential equation, Hemin, Sulfites, Applied mathematics, Physical and Theoretical Chemistry, Invariant (mathematics), Oxidoreductases, Constant (mathematics), Oxidation-Reduction, Hydrogen, Peroxidase |
| الوصف: | We present a numerical method to identify possible candidates for quasi-stationary manifolds in complex reaction networks governed by systems of ordinary differential equations. Inspired by singular perturbation theory, we examine the ratios of certain components of the reaction rate vector. Those ratios that rapidly approach a nearly constant value define a slow manifold for the original flow in terms of quasi-integrals, that is, functions that are nearly constant along the trajectories. The dimensionality of the original system is thus effectively reduced without reliance on a priori knowledge of the different time scales in the system. We also demonstrate the relation of our approach to singular perturbation theory which, in its simplest form, is just the well-known quasi-steady-state approximation. In two case studies, we apply our method to oscillatory chemical systems: the 6-dimensional hemin-hydrogen peroxide-sulfite pH oscillator and a 10-dimensional mechanistic model for the peroxidase-oxidase (PO) reaction system. We conjecture that the presented method is especially suited for a straightforward reduction of higher dimensional dynamical systems where analytical methods fail to identify the different time scales associated with the slow invariant manifolds present in the system. |
| تدمد: | 1520-5215 1089-5639 |
| DOI: | 10.1021/jp045665s |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59cff61026235d5914af29b1652665c1 https://doi.org/10.1021/jp045665s |
| رقم الانضمام: | edsair.doi.dedup.....59cff61026235d5914af29b1652665c1 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15205215 10895639 |
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| DOI: | 10.1021/jp045665s |