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Received October 20, 2005
Accepted January 13, 2006
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This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits
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Undamped oscillations in bacterial glycolysis models
Department of Chemical Engineering, National United University, Miao-Li 360, Taiwan
chuang@nuu.edu.tw
Korean Journal of Chemical Engineering, May 2006, 23(3), 419-427(9), 10.1007/BF02706744
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Abstract
The exotic dynamical behaviors exhibited in chemical reaction systems, such as multiple steady states, undamped oscillations, chaos, and so on, often result from unstable steady states. A bacterial glycolysis model is studied, which involves the generation of adenosine triphosphate (ATP) in a flow system and consists of eight species and ten reactions. A minimum subnetwork of the bacterial glycolysis model is determined to exhibit an unstable steady state with a positive real eigenvalue, which gives rise to undamped oscillations for a small perturbation. A set of rate constants and the corresponding unstable steady state are computed by using a positive real eigenvalue condition. The phenomena of oscillations and bifurcation are discussed. These results are extended to the bacterial glycolysis model and several parent networks.
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Horn FJM, Arch. Ration. Mech. Anal., 49, 172 (1972)
Horn FJM, Jackson R, Arch. Ration. Mech. Anal., 47, 81 (1972)
Hung YF, Schreiber I, Ross J, J. Phys. Chem., 99(7), 1980 (1995)
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Li HY, Chem. Eng. Sci., 53(21), 3703 (1998)
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Orban M, Epstein IR, J. Am. Chem. Soc., 107, 2302 (1985)
Schlosser PM, Feinberg M, Chem. Eng. Sci., 49(11), 1749 (1994)
