Example flux path in a toy metabolic network.

Pathway recovery analysis. (a) Average recovery rate among the k-shortest paths for k = 1, 5, 10, 100. (b) Average recovery rate among the k-shortest paths for k = 1,...,100 for different path-finding approaches.

Effect of stoichiometry in pathway recovery analysis. Average recovery rate among the k-shortest paths for k = 1,...,100 for CFP approach with and without considering stoichometry in (a) oxic conditions; and (b) anoxic conditions; (c) Average recovery rate among the k-shortest paths for k = 1, 5, 10, 100 for the CFP approach in oxic and anoxic conditions.

100 shortest CFPs in E. coli from Pyr to OAA in oxic conditions. Both the thickness of arcs and the size of metabolite nodes correspond to their frequency of appearance in the 100 shortest CFPs. Metabolites in grey are intermediates involved in the TCA cycle. See Additional file 3 for details.

Metabolite graph representation of the PEP: Pyr uptake system of glucose. (a) Metabolite graph; (b) metabolite graph restricted to atomic exchanges; (c) metabolite graph restricted to carbon exchanges. D-Glc, glucose; G6P, glucose 6-phosphate; PEP, phosphoenolpyruvate; Pyr, pyruvate.

Effect of carbon exchange and reversibility constraints. (a) De novo biosynthesis of pyrimidine ribonucleotides in E. coli discussed in Faust et al. [13]. (b) Shortest pathway from glucose to pyruvate in E. coli. 2DDG6P, 2-Dehydro-3-deoxy-D-gluconate 6-phosphate; 6PGC, 6-Phospho-D-gluconate; 6PGL, 6-phospho-D-glucono-1,5-lactone; AcCoA, Acetyl-CoA; ACCOAC, acetyl-CoA carboxylase; AcGlc-D, 6-Acetyl-D-glucose; ASPCT, aspartate carbamoyltransferase; CBASP, N-Carbamoyl-L-aspartate; CBP, Carbamoyl phosphate; CBPS, carbamoyl-phosphate synthase; CDP, cytidine-diphosphate; CTPS2, CTP synthase; D-Glc, D-Glucose; DHOr-S, (S)-Dihydroorotate; DHORTS, dihydroorotase; DHORD2, dihydoorotic acid dehydrogenase; EDA, 2-dehydro-3-deoxy-phosphogluconate aldolase; EDD, 6-phosphogluconate dehydratase; G6PDH2r, glucose 6-phosphate dehydrogenase; GLCATr, D-glucose O-acetyltransferase; G3P, Glyceraldehyde 3-phosphate; G6P, D-Glucose 6-phosphate; GLX, Glyoxylate; HCO3, Bicarbonate; HEX1, hexokinase; L-Asp, L-Aspartate; L-Glu, L-Glutamate; L-Gln, L-Glutamine; L-Mal, L-Malate; OMPDC, orotidine-5'-phosphate decarboxylase; ORPT, orotate phosphoribosyltransferase; MalCoa, Malonyl-CoA; MALS, malate synthase; ME1, malic enzyme; NDPK2, nucleoside-diphosphate kinase; NDPK3, nucleoside-diphosphate kinase; Orot, Orotate; Orot5P, Orotidine 5'-phosphate; PGL 6-phosphogluconolactonase; PRPP, 5-Phospho-alpha-D-ribose 1-diphosphate; Pyr, Pyruvate; UMPK, UMP kinase.

Simplified network from that presented in de Figueiredo et al. [25]considering the question of conversion of fatty acids to sugars. AcCoA, acetyl-CoA; AKG, 2-oxoglutarate; AKGDH, 2-oxogluterate dehydrogenase; Cit, citrate; CS, citrate synthase; D-Glc, glucose; D-Glc-ext, external glucose; Fum, fumarate; FUM, fumarase; G6P, glucose 6-phosphate; G6PP, glucose-6-phosphate phosphatase; GLCex, Glucose Exchange; Glx, Glyoxylate; ICDHyr, isocitrate dehydrogenase; ICit, isocitrate; ICL, Isocitrate lyase; L-Mal, Malate; MALS, malate synthase; MDH, malate dehydrogenase; ME1, malic enzyme (NAD); OAA, oxaloacetate; PC, Pyruvate carboxylase; PCK1, phosphoenolpyruvate carboxykinase; PDH, pyruvate dehydrogenase; PEP, phosphoenolpyruvate; PYK, pyruvate kinase; Pyr, pyruvate; SUCC, succinyl; SUCCoA, succinyl-coenzyme A; SUCDi, succinate dehydrogenase; SUCOAS, succinyl-CoA synthetase.

Effect of stoichiometry in connectivity analysis. (a) Connectivity curve for oxaloacetate (OAA). (b) Connectivity curve for arginine (L-Arg). (c) Connectivity curve for phosphatidic acid (PA120).

100 shortest CFPs in E. coli from Pyr to OAA in anoxic conditions. Both the thickness of arcs and the size of metabolite nodes correspond to their frequency of appearance in the 100 shortest CFPs. Metabolites in grey are intermediates involved in the TCA cycle. See Additional file 3 for details.