Explicit kinetic models, metabolic reactions

As outlined in the previous section, there is a hierarchy of possible representations of metabolism and no unique definition what constitutes a true model of metabolism exists. Nonetheless, mathematical modeling of metabolism is usually closely associated with changes in compound concentrations that are described in terms of rates of biochemical reactions. In this section, we outline the nomenclature and the essential steps in constructing explicit kinetic models of metabolic networks. 

As demonstrated in the work of Grimbs et al. [296] using a model of the human erythrocyte, the ranking obtained by any of the measures above is i) consistent independent of the specific measure and ii) corresponds closely to a ranking obtained from an explicit kinetic model of the pathway, and it is in excellent agreement with prior knowledge of the metabolic system. Consequently, we expect that the methods described here and in [296] provide a suitable starting point to locate crucial parameters and reactions in cellular metabolism, as well as in cases where the construction of explicit kinetic models is not (yet) feasible. 

To investigate these two questions, a parametric model of the Jacobian of human erythrocytes was constructed, based on the earlier explicit kinetic model of Schuster and Holzhiitter [119]. The model consists of 30 metabolites and 31 reactions, thus representing a metabolic network of reasonable complexity. Parameters and intervals were defined as described in Section VIII, with approximately 90 saturation parameters encoding the (unknown) dependencies on substrates and products and 10 additional saturation parameters encoding the (unknown) allosteric regulation. The metabolic state is described by the concentration and fluxes given in Ref. [119] for standard conditions and is consistent with thermodynamic constraints. 

The dependence (1 TP of v, on ATP is modeled as in the previous section, using an interval C [—00,1] that reflects the dual role of the cofactor ATP as substrate and as inhibitor of the reaction. All other reactions are assumed to follow Michaelis Menten kinetics with ()rs E [0, 1], No further assumption about the detailed functional form of the rate equations is necessary. Given the stoichiometry, the metabolic state and the matrix of saturation parameter, the structural kinetic model is fully defined. An explicit implementation of the model is provided in Ref. [84],... 

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