Klipp2002_MetabolicOptimization_linearPathway(n=2)

The model describes time dependent gene expression as a means to enable cells to adapt metabolic activity optimally based on environmental conditions. It uses a simple unbranched pathway and a constraint of fixed total enzyme. It calculates enzyme profiles at different times which optimise a performance function, and compares them to experimental data. The initial model is cell-type agnostic, while the experimeental data is from yeast.

This model is described in the article:

Prediction of temporal gene expression. Metabolic opimization by re-distribution of enzyme activities.
Klipp E, Heinrich R, Holzhütter HG.
Eur. J. Biochem. 2002 Nov; 269(22): 5406-5413

Abstract:

A computational approach is used to analyse temporal gene expression in the context of metabolic regulation. It is based on the assumption that cells developed optimal adaptation strategies to changing environmental conditions. Time- dependent enzyme profiles are calculated which optimize the function of a metabolic pathway under the constraint of limited total enzyme amount. For linear model pathways it is shown that wave-like enzyme profiles are optimal for a rapid substrate turnover. For the central metabolism of yeast cells enzyme profiles are calculated which ensure long-term homeostasis of key metabolites under conditions of a diauxic shift. These enzyme profiles are in close correlation with observed gene expression data. Our results demonstrate that optimality principles help to rationalize observed gene expression profiles.

This model is from the paper Prediction of temporal gene expression metabolic optimization by re-distribution of enzyme activities. The model describes optimal enzyme profiles and metabolite time courses for a simple linear metabolic pathway (n=2). Figure 1 was reproduced using roadRunner. The values of k1 and k2 were not explicitly stated in the publication, but calculations were performed for equal catalytic efficiencies of the enzymes (ki=k), hence the curator assigned k1=k2=1. Also enzyme concentrations are given in units of Etot; times are given in units of 1/(k*Etot) in the papaer, for simplicity , we use defalut units of the SBML to present the concentration and time.

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Le Novère Nicolas lenov@ebi.ac.uk EMBL-EBI Juty Nick juty@ebi.ac.uk EMBL-EBI He Enuo enuo@caltech.edu BNMC 2007-03-26T09:35:54Z 2015-02-25T12:24:34Z

Etot=E1+E2 is constant.

 species_5 species_2 compartment_0 species_0 species_2 k1 compartment_0 k2 species_1 species_3

During the initial phase, t smaller than T1 (T1=1), the whole amount of protein is allocated to the first reaction(E1=Etot, E2=0). At the beginning of the second phase the concentration E2 undergoes an abrupt switch from zero to a finite vaule whereas the concentration E1 is descreased by the same extent.

 time 1

at time=1, E1=0.4

 0.4