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Supplemental material 1 – Example network The reaction scheme in Figure C1 includes the tricarboxylic acid (TCA) cycle, glyoxylate shunt and adjacent amino acid metabolism. In this example, all cofactors, such as ATP and NAD+ were considered as external, as are 2-phospho-glycerate (PG), NH3 and CO2. A detailed description of the enzymes and metabolites is given in the legend of figure C1. The metabolic network for the demonstration of the proposed method was derived from Schuster et al. [1]. PG Pps Eno Pyk PEP AceEF Pyr AcCoA Ppc GltA OAA Pck Cit Acn Mdh AlaCon Icl Mal Glu AspC Gly Mas IsoCit Fum Ala IivE/AvtA Icd Pyr OG Asp AspCon AspA Fum OG Sdh Succ SucCD SucCoA Gdh GluCon Glu SucAB SucCoACon Figure C1: Reaction scheme consisting of the tricarboxylic acid cycle, glyoxylate shunt and some adjacent reactions of amino acid metabolism in Escherichia coli. Abbreviations of metabolites: AcCoA, acetyl-CoA; Ala, alanine; Asp, aspartate; Cit, citrate; Fum, fumarate; Glu, glutamate; Gly, glyoxylate; IsoCit, isocitrate; Mal, malate; OAA, oxaloacetate; OG, 2-oxoglutarate; PEP, phosphoenolpyruvate; PG, 2phosphoglycerate; Pyr, pyruvate; Succ, succinate; SucCoA, succinyl-CoA. Abbreviations of enzymes: AceEF, pyruvate dehydrogenase; Acn, aconitase; AspA, aspartase; AspC, aspartate aminotransferase; Eno, enolase; Fum, fumarase; Gdh, glutamate dehydrogenase; GltA, citrate synthase; Icd, isocitrate dehydrogenase (in E. coli with cofactors NADP/NADPH); Icl, isocitrate lyase; Mas, malate synthase; IlvE/AvtA, branched-chain amino acid aminotransferase/valine-pyruvate aminotransferase; Mdh, malate dehydrogenase; Pck, PEP carboxykinase (in E. coli with cofactors ADP/ATP); Ppc, PEP carboxylase; Pps, PEP synthetase; Pyk, pyruvate kinase; Sdh, succinate dehydrogenase; SucAB, 2-oxoglutarate dehydrogenase; SucCD, succinyl-CoA synthetase (in E. coli with cofactors ADP/ATP); AlaCon, AspCon, GluCon and SucCoACon, consumption of alanine, aspartate, glutamate and succinyl-CoA, respectively. Reversible reactions are indicated by double arrow-heads. 9 10 11 12 13 14 15 16 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 2 2 1 1 0 1 1 1 2 1 1 0 1 0 0 0 0 0 0 2 2 1 0 0 1 1 1 2 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 2 2 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 2 0 0 0 0 0 2 2 1 0 1 1 1 1 0 1 1 2 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 3 3 2 0 0 2 1 1 2 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 3 3 2 0 0 2 1 1 2 1 1 0 SucAB Icd 0 0 GltA Pck Ppc Acn 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 AceEF 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 Gdh IlvE/AvtA AlaCon GluCon AspA AspC Pps Pyk SucCD 8 Sdh 6 7 Fum 5 Mdh 3 4 Icl Mas 0 0 1 1 0 1 2 1 2 1 3 2 2 3 1 3 1 2 AspCon SucCoCon Eno No. Emodes All 16 elementary modes (for detail see [1]) were transformed in matrix notation: 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 The reactions (enzymes) are presented in the columns, the elementary modes in the rows. For the calculation of target validity for succinyl-CoA production (SucCoACon), only elementary flux modes with succinyl-CoA production were considered, which means that all rows with a zero entry in column SucCoACon were deleted. Hence, the matrix dimension decreased from a dimension 16 x 24 matrix (16 elementary modes; 24 reactions) to a 6 x 24 matrix, whereas only the elementary modes {8, 9, 10, 11, 13, 16} were further used for the calculation. The coefficients si,j of reactions i of each elementary mode j are normalized to the substrate coefficients sC,j (Eno) leading to the yield coefficients i,j. The modes have been arranged with increasing size of the succinyl-CoA yields SucCoACon (reaction: SucCoACon) as shown in 0 0 0 12 0 0 0 0 0 12 12 12 0 12 12 0 0 0 0 0 0 13 13 1 2 0 0 0 0 Icd 0 SucAB 13 0 Gdh IlvE/AvtA Sdh 13 12 12 12 12 SucCD Fum 23 13 13 23 0 Mas 0 12 0 Icl 23 0 1 Acn 1 1 Ppc 1 0 12 0 0 0 0 0 Pck 0 13 0 0 0 0 0 GltA Mdh AlaCon GluCon AspA AspC Pps SucCoCon AceEF 1 1 1 1 1 1 Pyk 16 9 13 11 8 10 Eno AspCon No. Emodes following matrix. 0 0 0 12 12 1 3 1 3 2 3 0 0 0 23 0 0 0 0 0 23 23 13 0 13 13 13 13 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 SucCoACon i The formation of interesting substances from succinyl-CoA can occur via the six different modes {8, 9, 10, 11, 13, 16}, whereas no co-production of glutamate, alanine and aspartate were observed. The modes {8, 10} offered the highest maximal theoretical yields for succinyl-CoA. Each of i were correlated as function of SucCoACon resulting in statistical evident correlations or not (Table C2). Statistical evaluation Table C2: Statistical analysis of simulation data for succinyl-CoA production with E. coli. R²: regression coefficient, alpha: slope-correlation coefficient, NOSTAT: no statistical evaluation. The values correspond to Figure 2a. The entries of ‘#DIV/0’ regarded to constant values (or complete zeros) of stoichiometric coefficients for the corresponding enzyme. Enzymes AspCon SucCoACon AlaCon GluCon AspA AspC Pps Pyk AceEF GltA Pck Ppc Acn Icl Mas Mdh Fum Sdh SucCD Gdh IIvE/AvtA SucAB Icd R² #DIV/0! 1 #DIV/0! #DIV/0! 0.3428571 0.3428571 #DIV/0! 0.8552036 0.8552036 1 #DIV/0! 0.8552036 1 0.3962264 0.3962264 0.621135 0.481203 1 0.8552036 0.3428571 #DIV/0! 0.3962264 0.3962264 alpha 0 1 0 0 0.8571429 0.8571429 0 -1.5 -1.5 -1 0 1.5 -1 -0.5 -0.5 -1.642857 -1.142857 -2 -1.5 0.8571429 0 -0.5 -0.5 evaluation correlation #DIV/0! #DIV/0! #DIV/0! #DIV/0! NOSTAT NOSTAT #DIV/0! -1.5 -1.5 -1 #DIV/0! 1.5 -1 NOSTAT NOSTAT NOSTAT NOSTAT #DIV/0! -1.5 NOSTAT #DIV/0! NOSTAT NOSTAT Reference 1. Schuster S, Dandekar T, Fell DA: Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends Biotechnol 1999, 17(2):53-60.