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Processes 2013, 1(3), 263-278; doi:10.3390/pr1030263
Article

Complex Nonlinear Behavior in Metabolic Processes: Global Bifurcation Analysis of Escherichia coli Growth on Multiple Substrates

 and *
Received: 2 July 2013; in revised form: 23 September 2013 / Accepted: 25 September 2013 / Published: 30 September 2013
(This article belongs to the Special Issue Feature Papers)
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Abstract: The nonlinear behavior of metabolic systems can arise from at least two different sources. One comes from the nonlinear kinetics of chemical reactions in metabolism and the other from nonlinearity associated with regulatory processes. Consequently, organisms at a constant growth rate (as experienced in a chemostat) could display multiple metabolic states or display complex oscillatory behavior both with potentially serious implications to process operation. This paper explores the nonlinear behavior of a metabolic model of Escherichia coli growth on mixed substrates with sufficient detail to include regulatory features through the cybernetic postulate that metabolic regulation is the consequence of a dynamic objective function ensuring the organism’s survival. The chief source of nonlinearity arises from the optimal formulation with the metabolic state determined by a convex combination of reactions contributing to the objective function. The model for anaerobic growth of E. coli was previously examined for multiple steady states in a chemostat fed by a mixture of glucose and pyruvate substrates under very specific conditions and experimentally verified. In this article, we explore the foregoing model for nonlinear behavior over the full range of parameters, γ (the fractional concentration of glucose in the feed mixture) and D (the dilution rate). The observed multiplicity is in the cybernetic variables combining elementary modes. The results show steady-state multiplicity up to seven. No Hopf bifurcation was encountered, however. Bifurcation analysis of cybernetic models is complicated by the non-differentiability of the cybernetic variables for enzyme activities. A methodology is adopted here to overcome this problem, which is applicable to more complicated metabolic networks.
Keywords: nonlinear analysis; non-smooth function; multiplicity; Escherichia coli; metabolic model; hybrid cybernetic model nonlinear analysis; non-smooth function; multiplicity; Escherichia coli; metabolic model; hybrid cybernetic model
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Song, H.-S.; Ramkrishna, D. Complex Nonlinear Behavior in Metabolic Processes: Global Bifurcation Analysis of Escherichia coli Growth on Multiple Substrates. Processes 2013, 1, 263-278.

AMA Style

Song H-S, Ramkrishna D. Complex Nonlinear Behavior in Metabolic Processes: Global Bifurcation Analysis of Escherichia coli Growth on Multiple Substrates. Processes. 2013; 1(3):263-278.

Chicago/Turabian Style

Song, Hyun-Seob; Ramkrishna, Doraiswami. 2013. "Complex Nonlinear Behavior in Metabolic Processes: Global Bifurcation Analysis of Escherichia coli Growth on Multiple Substrates." Processes 1, no. 3: 263-278.


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