The generalized flux-minimization method and its application to metabolic networks affected by enzyme deficiencies.

The flux-minimization method [Holzhütter, H.G., 2004. The principle of flux-minimization and its application to calculate stationary fluxes in metabolic networks. Eur. J. Biochem. 271, 2905-2922] has been proposed as an alternative to kinetic modeling to calculate stationary fluxes in metabolic networks. Here a generalization of this method is proposed that takes into account possible limitations of internal fluxes, e.g. due to enzyme defects or partial inhibition of enzyme activities by drugs. The generalized method consists in the minimization of an objective function which expresses the compromise that has to be made between minimization of internal fluxes on one hand and maintenance of the metabolic output required for various cellular functions on the other. Fulfillment of the latter condition is measured through a fitness function, which evaluates the relative deviation of the output fluxes from demanded target values. The method is applied to assess the metabolic consequences caused by a deficiency of enzymes involved in the metabolism of erythrocytes. The obtained results are in good agreement with those obtained on the basis of a comprehensive kinetic model.