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Supplementary Data

1. Chinese Hamster Ovary (CHO)
The model and reported flux distribution are cited from Llaneras and Pico (2007).
Llaneras, F. Pico, J. An interval approach for dealing with flux distributions and elementary modes activity patterns. J. Theor.
Biol. 2007, 246, 290-308.
Table S1 Prediction results for the flux distribution of CHO cells by Quadratic programming (QP) , the maximum entropy
principle (MEP), and Linear Programming in Enzyme Control Flux (ECFLP)
<==> reversible reaction; => irreversible reaction. Exp: Experimental fluxes. Metabolites: G, Glucose; L, Lactate; NH4, Ammonia; PU, Purine; Q, Glutamine; A, Alamime; CO2, Carbon Dioxide; PY, Pyrimidine; G6P, Glucose-6-phosphate; DAP, Dihydroxy-acetone Phosphate; R5P, Ribose-5-Phosphate; Cit, Citrate; Mal, Malate; Glu, Glutamate; G3P, Glyceraldehyde-3-phosphate; PYR, pyruvate; ACA, acetyl-coenzyme A; OXA, Oxaloacetate; AKG, α-ketoglutarase; ASP, Aspartate; GX, extracellular glucose; LX, extracelluar lactate; NH4X, extracellular ammonia; PUX, product purine; QX, extracellular glutamine; AX, extracellular alanine; CO2X, extracellular carbon dioxide; PYX, product 2. Escherichia coli The experimental flux distribution is cited from Burgard and Maranas (2003) Burgard, A.P., Maranas, C.D. Optimization-based framework for inferring and testing hypothesized metabolic objective functions. Biotechnol. Bioeng. 2003, 82, 670-677. The external flux for acetate is set to be 0 and glucose uptake is set to be 115 under aerobic conditions. The prediction results are shown in Table S2. Under anaerobic conditions, the external fluxes for acetate, ethanol, lactate and succinate are set to be 34.1, 65.3, 69.8 and 3.9, respectively. The uptake of glucose is set to be 115. The prediction results are shown in Table S3. Table S2 Prediction results for the flux distribution of E. coli under aerobic conditions by Quadratic programming (QP), Linear programming (LP) , the maximum entropy principle (MEP) and Linear Programming in Enzyme Control Flux (ECFLP) ACCOA + 0.165 GAP + 0.537 PEP + 0.982 P5P + 0.106 F6P + 1.979 OAA + 0.439 E4P + 1.207 AKG + 1.485 P3G ==> 1.677 CO2 <==> reversible reaction; => irreversible reaction. Exp: Experimental fluxes; Metabolites: G6P, glucose-6-phosphate; ACCOA , acetyl-coenzyme A; CO2, carbon dioxide; S7P, sedoheptulose-7-phosphate; PEP, phosphoenolpyruvate; P5P, pentose-5-phosphate; SUC, succinate; OAA, oxaloacetate; ICIT, isocitrate; P3G, 3-phosphoglycerate; LAC, lactate; PYR, pyruvate; ETH, ethanol; GAP, glyceraldehydes-3-phosphate; D6PGL, d-6-phosphate gluconate; MAL, malate; F6P, fructose-6-phosphate; AC, acetate; GLC, glucose; FUM, fumarate; E4P, erythrose-4-phosphate; AKG, α-ketoglutarase; ACEXT, external acetate; BIOMASS, biomass; GLCXT, external glucose; CO2EXT, Table S3 Prediction results for the flux distribution of Escherichia coli under anaerobic conditions by Quadratic programming (QP), Linear programming (LP), the maximum entropy principle (MEP), and Linear Programming in Enzyme Control Flux (ECFLP) 0.537 PEP + 0.982 P5P + 1.979 OAA + 1.485 P3G + 3.058 PYR + 0.165 GAP + 0.106 F6P + 0.439 E4P + 1.207 AKG ==> 1.677 CO2 + BIOMASS <==> reversible reaction; => irreversible reaction. Exp: Experimental fluxes; Metabolites: G6P, glucose-6-phosphate; ACCOA , acetyl-coenzyme A; CO2, carbon dioxide; S7P, sedoheptulose-7-phosphate; PEP, phosphoenolpyruvate; P5P, pentose-5-phosphate; SUC, succinate; OAA, oxaloacetate; ICIT, isocitrate; P3G, 3-phosphoglycerate; LAC, lactate; PYR, pyruvate; ETH, ethanol; GAP, glyceraldehydes-3-phosphate; D6PGL, d-6-phosphate gluconate; MAL, malate; F6P, fructose-6-phosphate; AC, acetate; GLC, glucose; FUM, fumarate; E4P, erythrose-4-phosphate; AKG, α-ketoglutarase; ACEXT, external acetate; BIOMASS, biomass; SUCEXT, external succinate; ETHEXT , external ethanol; GLCXT, external glucose; LACEXT, external lactate; CO2EXT, external carbon dioxide. 3. Saccharomyces cerevisiae The experimental flux distribution is cited from Frick and Wittmann (2005). Frick, O., Wittmann, C. Characterization of the metabolic shift between oxidative and fermentative growth in Saccharomyces cerevisiae by comparative 13C flux analysis, Microb Cell Fact, 2005, 4, 30. The external fluxes of glucose, acetate, ethanol and glycerol are set to be the same value as the experimental data. Metabolites (Table S4-S6): R5P, ribose-5-phosphate; G6P, glucose-6-phosphate; CO2, carbon dioxide; S7P, sedoheptulose-7-phosphate; PEP, phosphoenolpyruvate; ACE, acetate; ACCOACYT, cytosolic acetyl-coenzyme A; SUC, succinate; DHAP, dihydroxyacetong phosphate; SUCCOA, succinyl-coenzyme A; OAA, cytosolic oxaloacetate; P3G, 3-phosphoglycerate; PYR, cytosolic pyruvate; P6G, 6-phospho-gluconate; GA3P, glyceraldehydes-3-phosphate; MAL, malate; G15L, 6-phospho-glucono-1,5-lactone; RU5P, ribulose-5-phosphate; ACA, acetate; ICI, isocitrate; OAAMIT, mitochondrial oxaloacetate ; F6P, fructose-6-phosphate; ACCOAMIT, mitochondrial acetyl-coenzyme A; PYRMIT, mitochondrial pyruvate; X5P, xylulose-5-phosphate; GP, glycerone-3-phosphate; E4P, erythrose-4-phosphate; FUM, fumarate; AKG, α-ketoglutarase; ACEX, external acetate; CO2EX, external carbon dioxide; BIOMASS, biomass; ETH, ethanol; GLYC, glycerol; GLC, glucose; ETHEXT, external ethanol; GLCEXT, external glucose; GLYCEXT, external glycerol. <==> reversible reaction; => irreversible reaction. Exp: Experimental fluxes; Table S4. Prediction results for the flux distribution of Saccharomyces cerevisiae (µ=0.15 h-1) by Quadratic programming (QP), Linear programming (LP), the maximum entropy principle (MEP), and Linear Programming in Enzyme Control Flux (ECFLP) ACCOACYT + 10 OAA + 6 P3G + 3 ACCOAMIT + 18 PYRMIT + GP + 3 E4P + 11 AKG ==> 100 BIOMASS Table S5. Prediction results for the flux distribution of Saccharomyces cerevisiae (µ=0.30 h-1) by Quadratic programming (QP), Linear programming (LP), the maximum entropy principle (MEP), and Linear Programming in Enzyme Control Flux (ECFLP) ACCOACYT + 10 OAA + 6 P3G + 3 ACCOAMIT + 18 PYRMIT + GP + 3 E4P + 11 AKG ==> 100 BIOMASS Table S6. Prediction results for the flux distribution of Saccharomyces cerevisiae (µ=0.40 h-1) by Quadratic programming (QP), Linear programming (LP), the maximum entropy principle (MEP) , and Linear Programming in Enzyme Control Flux (ECFLP) ACCOACYT + 10 OAA + 6 P3G + 3 ACCOAMIT + 18 PYRMIT + GP + 3 E4P + 11 AKG ==> 100 BIOMASS

Source: http://www.cadlive.jp/MetabolicEngineering/MEP/SupplementaryData.pdf