Development of kinetic models for large and complex metabolic networks is a primary aim of systems biology. However, with increasingly involved systems, the demands on experimental knowledge regarding kinetic rate laws and parameters is also largely enhanced. To cope with the problem of missing information on parts of the networks, we develop methods to reduce complexity of networks without losing predictive power. Another ambitious aim is the integration of models of metabolism, signal transduction, gene expression and protein translation.
Fig. 1, Fig. 2 and Table 1 show how kinetic hybrid models composed of mechanistic and simplified enzymatic rate laws speed up the kinetic modeling of complex metabolic networks (Bulik et al., 2009).
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| Fig. 1 Erythrocyte energy metabolism. Reaction scheme of erythrocyte energy metabolism comprising glycolysis, the pentose phosphate shunt and provision of reduced GSH. The ATPase and GSH oxidase reactions are overall reactions representing the total ATP demand and reduced GSH consumption. 1,3PG, 1,3-bisphosphoglycerate; 2,3PG, 2,3-bisphosphoglycerate; 2PG, 2-phosphoglycerate; 3PG, 3-phosphoglycerate; 6PG, 6-phosphoglycanate; 6PGD, 6-phosphogluconate dehydrogenase; AK, adenylate kinase; ALD, aldolase; DPGase, 2,3-bisphosphoglycerate phosphatase; DPGM, 2,3-bisphosphoglycerate mutase; E4P, erythrose 4-phosphate; EN, enolase; EP, ribose phosphate epimerase; Fru1,6P2, fructose 1,6-bisphosphate; Fru6P, fructose 6-phosphate; G6PD, glucose-6-phosphate dehydrogenase; Glc6P, glucose 6-phosphate; GlcT, glucose transport; GPI, glucose-6-phosphate isomerase; GraP, glyceraldehyde 3-phosphate; GrnP, dihydroxyacetone phosphate; GSHox, glutathione oxidase; GSSG, oxidized glutathione; GSSGR, glutathione reductase; HK, hexokinase; KI, ribose phosphate isomerase; LAC, lactate; LACT, lactate transport; LDH, lactate dehydrogenase; PEP, phosphoenolpyruvate; PFK, phosphofructokinase; PGK, phosphoglycerate kinase; PGM, 3-phosphoglycerate mutase; PK, pyruvate kinase; PRPP, phosphoribosyl pyrophosphate; PRPPS, phosphoribosylpyrophosphate synthetase; PRPPT, phosphoribosylpyrophosphate transport; PYR, pyruvate; Rib5P, ribose 5-phosphate; Ru5P, ribulose 5-phosphate; S7P, sedoheptulose 7-phosphate; TA, transaldolase; TK, transketolase; TPI, triose phosphate isomerase; Xul5P, xylulose 5-phosphate. | Fig. 2 Erythrocyte energetic load characteristics. The diagrams show the total rate of ATP consumption versus the energetic load given as percentage of the energetic load kATPase = 1.6 mM of the reference state. Each diagram shows the load characteristics calculated by means of the mechanistic model (blue line), the approximate model fully based on simplified rate laws (red line), and the hybrid model (green line). Unstable steady states are indicated by dotted lines. |
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Table 1. Simplified rate expressions used in the kinetic model of erythrocyte metabolism. Si and Pi denote the concentrations of the reaction substrates and products, respectively. The integer constants μi and νi are the stoichiometric coefficients with which the ith substrate and product enter the reaction. K denotes the thermodynamic equilibrium constant and k the catalytic constant of the subject enzyme, and ν the flux of the reaction. The empirical parameters ai and bi have different meanings in the PL, LL and MM rate laws. The notation of the PL rate equation differs from the conventional form in that the rate is here decomposed into an MA term and a residual PL term. Hence, the PL exponents for substrates and products commonly used in most applications correspond to ai + μi and bi + νi. The form of the MM equation used is based on the assumption that all μi substrate molecules and νi product molecules bind simultaneously (and not consecutively and not cooperatively) to the enzyme. |
Researchers
Sascha Bulik
Matthias König
Prof. Hermann-Georg Holzhütter
in cooperation with S. Grimbs and Prof. J. Selbig, Department of Bioinformatics, Max Planck Institute for Molecular Plant Physiology, Potsdam-Golm and Institute of Informatics, University Potsdam
Own Publications
Bulik S, Grimbs S, Huthmacher C, Selbig J, Holzhütter HG. (2009) Kinetic hybrid models composed of mechanistic and simplified enzymatic rate laws: A promising method for speeding up the kinetic modelling of complex metabolic networks. FEBS Journal, 276:410-424 [PubMed]
Grimbs S, Selbig J, Bulik S, Holzhütter HG, Steuer R. (2007) The stability and robustness of metabolic states: identifying stabilizing sites in metabolic networks. Mol Syst Biol., 3:146. [PubMed]