Fig 1.
The conceptual basis of p13CMFA.
From an infinite space of flux (v) solutions, a space of feasible solutions is obtained through the integration of stoichiometric and thermodynamic constraints (in the form of a constraint-based model) and the measured extracellular fluxes. Applying 13C MFA to integrate experimental 13C data can further reduce the solution space to those flux distributions that are consistent with such data. Through flux minimization, p13CMFA can identify the optimal flux distribution that lies on the edge of the 13C MFA solution space. Such minimization can be weighted according to the gene expression evidence for each enzyme.
Fig 2.
Flux spectrum, GIMME solutions, 13C MFA flux ranges, and p13CMFA solutions for some key reaction fluxes in the HUVECs case study.
Flux spectrum represents the feasible flux ranges considering only the stoichiometric and thermodynamic constraints and the measured extracellular fluxes. GIMME flux values are obtained when total reaction flux is minimized weighted by gene expression without integrating 13C data. For 13C MFA, the flux values obtained after the 13C MFA optimization and the range of the 95% confidence intervals for such values are shown. The p13CMFA flux values are obtained when total reaction flux is minimized within the 13C MFA solution space. Fluxes are expressed in μmol·h-1·million-cells-1.
Fig 3.
Schematic representation of the central carbon metabolism flux map obtained with p13CMFA in the HUVECs case study.
Reaction fluxes are indicated for some key reactions in μmol·h-1·million-cells-1. Arrows indicate net flux direction, and line width is representative of flux magnitude. Reactions and metabolites of redox and energy metabolism have been omitted from this figure for clarity. 2PG: 2-Phosphoglycerate. 3PG: 3-Phosphoglycerate. AcCoA: Acetyl-CoA. aKG: α-Ketoglutarate. Asp: Aspartate. bPG13: 1,3-Bisphosphoglycerate. Cit: Citrate. DhaP: Dihydroxyacetone phosphate. Fru16bP: Fructose 1,6-bisphosphate. Fru6P: Fructose 6-phosphate. Fum: Fumarate. GaP: Glyceraldehyde-3-Phosphate. Glc: Glucose. Glc1P: Glucose 1-phosphate. Glc6P: Glucose 6-phosphate. Gln: Glutamine. Glu: Glutamate. Glucon6P: Gluconate 6-phosphate. Glygn: Glycogen. iCit: Isocitrate. Lac: Lactate. Mal: Malate. OAA: Oxaloacetate. PEP: Phosphoenolpyruvate. Pyr: Pyruvate. Rib5P: Ribose 5-phosphate. Rul5P: Ribulose 5-phosphate. Sed7P: Sedoheptulose 7-phosphate. Suc: Succinate. SucCoa: Succinyl-CoA. UDPGlc: Uridine diphosphate glucose. The subscripts e, c, and m denote the extracellular, cytosolic and mitochondrial compartments, respectively.
Fig 4.
Comparison of the predictive power of 13C MFA, pFBA, GIMME, and p13CMFA.
A: Pearson’s correlation coefficients between the reference flux distribution and the flux maps obtained from 13C MFA (optimal solution), pFBA, GIMME, and p13CMFA. p13CMFA was applied both with and without integrating gene expression data (p13CMFA+ge and p13CMFA-ge, respectively). The statistical significance of the difference between correlation coefficients was evaluated using the Fisher r-to-z transformation[33]. B: Euclidian distances between the reference flux distribution and the flux maps obtained from 13C MFA (optimal solution), pFBA, GIMME, and p13CMFA.