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

Abstract

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. OPEN ACCESSProcesses 2013, 1 264

Toward intensifying design of experiments in upstream bioprocess development: An industrial Escherichia coli feasibility study

“…Despite the respectable results obtained in this feasibility study, it should be mentioned that dynamic variations in process conditions can result in transitions between intracellular (steady) states . While these transitions can occur during constant process conditions, simultaneous excitations in pH, temperature, and the feeding rate might be more likely to provoke state transitions, since these process variables are interconnected …”

“…This behavior could have been a contributing factor in batches III, [c], and [k], where the productivity was under‐predicted. To verify these mispredictions are due to state transitions, other extracellular metabolites such as acetate, pyruvate, lactate or succinate and/or the activity of certain enzymes should be measured. Batches conducted in a process condition space that includes a meta‐stable transition zone will likely have cultures go through different cellular states.…”

Special Issue “Feature Papers”

“…The first paper in this area concerns the development of a mathematical model of a multi-stage flash desalination process that is used to minimize the total daily operating cost by optimizing the number of stages, seawater rejected flowrate and brine recycle flowrate [5]. In the second paper, a cybernetic model of Escherichia coli growth on mixed substrates is OPEN ACCESS subjected to bifurcation analysis and theoretically shown to exhibit a steady-state multiplicity up to seven [6]. The third paper reviews the history of Chinese hamster ovary (CHO) cells commonly used to manufacture protein pharmaceuticals and argues that CHO cells are a prototypical example of a "quasispecies" due to their exposure to high mutation rate environments [7].…”

New Biosorbent Materials: Selectivity and Bioengineering Insights

“…However, some changes in the symbols and the physical meanings differentiate the models and give other potential to the whole engineering part. Models are used everywhere for simulating any possible process [54][55][56][57][58][59][60][61][62][63][64][65][66]. The main models, which will be discussed in following, are the Freundlich, Langmuir, and Langmuir-Freundlich (L-F) equations.…”