Structural kinetic modeling

In this section, we describe a recently proposed approach that aims overcome some of the difficulties [23, 84, 296, 325] Structural Kinetic Modeling (SKM) seeks to provide a bridge between stoichiometric analysis and explicit kinetic models of metabolism and represents an intermediate step on the way from topological analysis to detailed kinetic models of metabolic pathways. Different from approximative kinetics described above, SKM is based on those properties that are a priori independent of the functional form of the rate equation. 

Structural kinetic modeling keeps the advantages of the stoichiometric analysis, while incorporating dynamic aspects into the description of the system. 

Figure 25. Structural Kinetic Modeling seeks to keep the advantages of stoichiometric analysis, while incorporating dynamic properties into the description of the system. Specifically, SKM aims to give a quantitative account of the possible dynamics of a metabolic network.

Figure 26. The proposed workflow of structural kinetic modeling Rather than constructing a single kinetic model, an ensemble of possible models is evaluated, such that the ensemble is consistent with available biological information and additional constraints of interest. The analysis is based upon a (thermodynamically consistent) metabolic state, characterized by a vector S° and the associated flux v° v(S°). Since based only on the an evaluation of the eigenvalues of the Jacobian matrix are evaluated, the approach is (computationally) applicable to large scale system. Redrawn and adapted from Ref. 296.

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],... 

Evaluating the structural kinetic model, we first consider the possibility of sustained oscillations. Starting with the simplest scenario, all saturation parameters are set to unity, corresponding to bilinear mass-action kinetics and... 

The construction of the structural kinetic model proceeds as described in Section VIII.E. Note that in contrast to previous work [84], no simplifying assumptions were used the model is a full implementation of the model described in Refs. [113, 331]. The model consists of m = 18 metabolites and r = 20 reactions. The rank of the stoichiometric matrix is rank (N) = 16, owing to the conservation of ATP and total inorganic phosphate. The steady-state flux distribution is fully characterized by four parameters, chosen to be triosephosphate export reactions and starch synthesis. Following the models of Petterson and Ryde-Petterson [113] and Poolman et al. [124, 125, 331], 11 of the 20 reactions were modeled as rapid equilibrium reactions assuming bilinear mass-action kinetics (see Table VIII) and saturation parameters O1 1. 

R. Steuer, T. Gross, J. Selbig, and B. Blasius, Structural kinetic modeling of metabolic networks. Proc. Natl. Acad. Sci. USA 103(32), 11868 11873 (2006). 

Batt BC, Kompala DS (1989), A structured kinetic modeling framework for the dynamics of hibrodoma growth and monoclonal antibody production in continuous suspension cultures, Biotechnol. Bioeng. 34 515-531... 

Assume an experiment in which a group of subjects selected to represent a spectrum of severity of some condition (e.g., renal insufficiency) is given a dose of drug, and drug concentrations are measured in blood samples collected at intervals after dosing. The structural kinetic models used when performing a population analysis do not differ at all from those used for analysis of data from an individual patient. One still needs a model for the relationship of concentration to dose and time, and this relationship does not depend on whether the fixed-effect parameter changes... 

Koller, M., Horvat, P., Hesse, P.l. et al. (2006) Assessment of formal and low structured kinetic modeling of polyhydroxyalkanoate synthesis from complex substrates. Bioprocess and Biosystems Engineering, 29(5-6), 367-377. 

Keywords. Computational fluid dynamics (CFD), Intracellular metabolites. Integration of CFD with imstructmed and structured kinetic models... 

MetabolicaUy Structured Models Stimulated by Dynamically Changing Environment - Integration of CFD and Structured Kinetic Models. 61... 

To a large extent, the formal kinetic analysis techniques presented in this chapter relate to discontinuous batch operations. Even if the goal is a continuous operation, the batch process kinetic model serves as a start-up. The most significant element of a kinetic analysis is the time dependence of the macroscopic process variables mentioned in Chap. 2. Bacteria, molds, viruses, and yeasts all have different reproduction mechanisms, and formulating a structured kinetic model more closely related to the actual mechanism is a desirable goal. More structured models are desirable not only to deal with active cells but also to extend kinetic analysis to more complex situations involving inactive cells, mixed populations of cells, multiple substrates, and... 

Steuer R, Gross T, Selbig J, Blasius B (2006) Structural kinetic modeling of metabolic networks. Proc Natl Acad Sci U S A 103 11868-11873... 

DBsolve is a standalone software tool for the construction and analysis of mathematical models of biological systems. It helps in the automatic generation of structural kinetic models on the basis of stoichiometric matrices or reaction lists, numerical parameter... 

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