Dynamical reduction of linearized metabolic networks through quasi steady state approximation

Metabolic modeling has gained accuracy in the last decades, but the resulting models are of high dimension and difficult to use for control purpose. Here we propose a mathematical approach to reduce high dimensional linearized metabolic models, which relies on time scale separation and the quasi ste...

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Bibliographic Details
Published in:AIChE journal 2019-01, Vol.65 (1), p.18-31
Main Authors: López Zazueta, Claudia, Bernard, Olivier, Gouzé, Jean‐Luc
Format: Article
Language:English
Subjects:
Automatic Control Engineering
Computer Science
Differential equations
Linearization
Mathematical models
metabolic modeling
Metabolic networks
Metabolism
Metabolites
microalgae
Model accuracy
Organic chemistry
Parameter estimation
Reduction
slow‐fast analysis
Steady state
Tikhonov theorem
unbalanced growth
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Summary:Metabolic modeling has gained accuracy in the last decades, but the resulting models are of high dimension and difficult to use for control purpose. Here we propose a mathematical approach to reduce high dimensional linearized metabolic models, which relies on time scale separation and the quasi steady state assumption. Contrary to the flux balance analysis assumption that the whole system reaches an equilibrium, our reduced model depends on a small system of differential equations which represents the slow variables dynamics. Moreover, we prove that the concentration of metabolites in quasi steady state is one order of magnitude lower than the concentration of metabolites with slow dynamics (under some flux conditions). Also, we propose a minimization strategy to estimate the reduced system parameters. The reduction of a toy network with the method presented here is compared with other approaches. Finally, our reduction technique is applied to an autotrophic microalgae metabolic network. © 2018 American Institute of Chemical Engineers AIChE J, 65: 18–31, 2019
ISSN:0001-1541
1547-5905
DOI:10.1002/aic.16406