Fig 1.
Example of how ODEs are automatically built for isotopomers and metabolites consumed or produced by the pyruvate dehydrogenase catalysed reaction (PDH).
PDH irreversibly transforms mitochondrial pyruvate (mPyr), NAD (mNAD), and coenzyme A (mCoA) into mitochondrial acetyl-CoA (mACoA) and NADH (mNADH). The system of differential equations is solved taking into account all equations for total concentrations of metabolites and for concentrations of isotopomers. From the previous step in the simulation, the PDH flux (Jpdh) is computed, which is a function of the concentrations of the reactants and products (m) and the kinetic parameters of PDH (p). For the ODEs describing the concentration of metabolites the computed value is added (+ =) and subtracted (- =) for products and substrates, respectively. For the ODE describing a particular isotopomer, the flux value is scaled according to the relative abundance of the isotopomer for the substrate (mPyri) and the resulting scaled flux (JPDHi) is added (+ =) and subtracted (- =) to d[mACoAi]/dt and d[mPyri]/dt, respectively. Isotopomers are not simulated for CoA, NAD or NADH because it is assumed that 13C from labelled substrates does not propagate to such metabolites.
Fig 2.
Schematic representation of the metabolic network used in the model.
In this representation, reactions associated with the glycolytic and gluconeogenic pathways are coloured in blue, reactions associated with glycogen metabolism are coloured in purple, reactions associated with the pentose phosphate pathway are coloured in pink, reactions associated with the Krebs cycle are coloured in orange, reactions associated with fatty acid metabolism are coloured in red and other reactions associated with redox and energy metabolism are coloured in green. Specifically, the reactions id of each reaction represented are 1:glctr, 2: gka, 3 g6pasea, 4: gkb, 5: g6paseb, 6: gpia, 7: gpib, 8: pfkla1, 9: fbasea1, 10: pfklb1, 11: fbaseb1, 12: pfkla2, 13: fbasea2, 14: pfklb2, 15: fbaseb2, 16: aldo1, 17: aldo2, 18: aldo3, 19: tim, 20: trik, 21: fruhk, 22: frutr, 23: gapdh, 24: pgk, 25: pgm, 26: eno, 27: pepck, 28: pk, 29: ldh, 30: lactr, 31: pyrtr, 32: mpyrtr, 33: pc, 34: dic, 35: pglm, 36: ugt, 37: gs, 38: gp, 39: g6pdh, 40: pgndh, 41: rpi, 42: rul5pepi, 43: tk1, 44: tk2, 45: tk3, 46: ta, 47: pdh, 48: cs, 49: aco, 50: idh, 51: kdh, 52: scs, 53: sdh, 54: fh, 55: mmdh, 56: malic, 57: citmtr, 58: citly, 59: acoacar, 60: fasyn, 61: box, 62: aatc, 63: aspglumtrans, 64: aatm, 65: malkgmtrans, 66: cmdh, 67: transa, 68: glutr, 69: glyc3pcdh, 70: glyc3pmdh, 71: nadhdh, 72: coqhoxi, 73: atpase, 74: pimtr, 75: pitr, 76: ppase, 77: atpmtrans, 78: cndk1, 79: cndk2, 80: mndk and 81 adk. Invisible reactions are not shown for clarity. The full lists of metabolites and reactions can be found on S1 and S2 Tables respectively.
Fig 3.
Bar graphs representing the experimentally determined metabolite productions (3.A) and isotopologue fractions (3.B) in experimental conditions.
Measurements were taken after incubating hepatocytes for 2 hours with 20 mM glucose 50% enriched in [1,2-13C2]-glucose and 3 mM fructose (condition A1), 20 mM glucose and 3 mM fructose 50% enriched in [U-13C6]-fructose (condition A2) and 20 mM glucose 50% enriched in [1,2-13C2]-glucose and 20 mM fructose (condition B). The red dot indicates the value fractions simulated by HepatoDyn using the best fit parameter set. Results of the isotopologue fractions are reported as m0, m1, m2, etc. where m0, m1, m2… indicate the number of 13C atoms in the isotopologue fractions of a given metabolite.
Fig 4.
Plot of the simulated concentrations over time for extracellular fructose (eFru), fructose 1-phosphate (Fru1P), cytosolic phosphate (cPi) and cytosolic ATP (cATP).
Specifically, the simulated concentrations in hepatocytes incubated with 20 mM glucose and 3 mM fructose (conditions A1 and A2, described in the main text) or 20 mM glucose and 20 mM fructose (condition B, described in the main text) are shown. The red plot indicates the values predicted with the best fit parameter set and the grey area indicates the estimated range of variations taking parameter sets within the 95% confidence intervals derived from the identifiability analysis.