Model Identification, Parameter Estimation, and Dynamic Flux Analysis of E. coli Central Metabolism

S. Čerić and Ž. Kurtanjek

Abstract
In this work are applied three global optimisation algorithms for adaptation of the mathematical model of the central metabolism of Escherichia coli to data obtained in the experiment with response to glucose impulse. Applied is the adaptive simplex method by Nelder-Mead, evolutionary algorithms of differential evolution, and simulated annealing. The original model has been modified by the following steps: closure of Entner-Doudoroff pathway with pyruvate balance, introduction of phosphoenolpyruavate carboxylase and carboxykinase reactions in the balance of phosphoenolypyravate, account for loss of pyruvate in biomass synthesis, change in kinetic rate expressions for several enzymes, and partial re-estimation of the kinetic parameters by the global optimisation algorithms. The modified model correctly predicts observed oscillatory response to glucose impulse in concentrations of pyruvate and D-ribose-5-phosphate. To discern metabolic control, evaluated are dynamic intracellular fluxes by the model simulation around the following network branching metabolites: α-D-glucose-6-phosphate, 6-phospho-D-gluconate, glyceraldehydes-3-phosphate, and pyruvate. The simulation of the fluxes around phosphoenolypyruvate show that phosphoenolpyruavate carboxylase and carboxykinase (PEPCK) activity and phosphotransferase system (PTS) are closely dynamically tied, indicating that glycolysis and TCA metabolisms can not be separated under the given transient conditions. Overall model adequacy is evaluated by standard deviations of the model predictions and experimental data for each metabolite.

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Keywords
Escherichia coli, central metabolism, glucose impulse, dynamic metabolic flux analysis, Global optimization