Non-stationary Metabolic Control Analysis of E. coli Central Metabolism by a Mathematical Model Simulation

A. Jurinjak Tušek and Ž. Kurtanjek

Abstract
A non-stationary metabolic control analysis (MCA) of E. coli central metabolism upon a response to a glucose impulse with an aim to discern the enzyme level regulation is applied. Results are obtained by a mathematical model simulation of the kinetic model derived from experimental data with a glucose impulse introduced after a 30-minute period of deprivation. The model includes 10 coupled metabolite balances, 24 highly nonlinear enzyme kinetic rate expressions and 132 kinetic parameters. Determined are the time courses of the flux control coefficients of the four fluxes (phosphotransferase system (PTS), nucleotide synthesis (NS), pyruvate and phosphoenolpyruvate to biomass) during the period of the first 15 seconds upon introduction of the impulse. Two methods, local and global, sensitivities of analysis are applied and compared. The local flux control coefficients are calculated by the finite difference formula for approximation of local derivatives applied one-by-one for each of the 24 enzyme levels (activities). The flux control coefficients based on global sensitivities are evaluated on the basis of partial variances corresponding to each enzyme under simultaneous variations of the all enzymes. Assumed are uniform probabilities of variations of the enzyme activities in the ranges (1 to 2) and (1 to 4) fold. The variances are calculated by the Fourier amplitude sensitivity test (FAST) numerical procedure. The two methods yielded similar overall features of the metabolic control, however identification of the key enzymes for particular fluxes are different. The results are an effort to broaden the scope of rational methodologies in application of genetic engineering.

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Keywords
Non-stationary MCA, global sensitivity, E. coli central metabolism