(* Generated by JWS Online *) (* This is an experimental feature of JWS Online. Please report any mistakes.*) (* Note that the following notable SBML entities or features are not supported in notebook outputyet: *) (* Events *) (* Constraints *) (* Units and UnitDefinitions *) (* AlgebraicRules *) (* conversionFactors *) variables = { adpPF[t], atpPF[t], b13pgPF[t], dhapPF[t], f16bpPF[t], f6pPF[t], g3pPF[t], g6pPF[t], gapPF[t], glcEX[t], glcPF[t], glyEX[t], lacEX[t], lacPF[t], nadPF[t], nadhPF[t], p2gPF[t], p3gPF[t], pepPF[t], pyrEX[t], pyrPF[t] }; initialValues = { adpPF[0] == 0.042, atpPF[0] == 0.042, b13pgPF[0] == 0.0028, dhapPF[0] == 0.0028, f16bpPF[0] == 0.0028, f6pPF[0] == 0.0028, g3pPF[0] == 0.0028, g6pPF[0] == 0.0028, gapPF[0] == 0.0028, glcEX[0] == 13.1884, glcPF[0] == 0.0028, glyEX[0] == 9.999998792799998*^-8, lacEX[0] == 9.999998792799998*^-8, lacPF[0] == 0.0028, nadPF[0] == 0.042, nadhPF[0] == 0.042, p2gPF[0] == 0.0028, p3gPF[0] == 0.0028, pepPF[0] == 7/25000, pyrEX[0] == 9.999998792799998*^-8, pyrPF[0] == 0.0028 }; rates = { vPFvALD, vPFvATPASE, vPFvENO, vPFvG3PDH, vPFvGAPDH, vPFvGLCtr, vPFvGLYtr, vPFvHK, vPFvLACtr, vPFvLDH, vPFvPFK, vPFvPGI, vPFvPGK, vPFvPGM, vPFvPK, vPFvPYRtr, vPFvTPI }; rateEquations = { vPFvALD -> (VPFvALD*f16bpPF[t]*(1 - (dhapPF[t]*gapPF[t])/(KeqPFvALD*Vpf*f16bpPF[t])))/(Kf16bpPFvALD*(1 + dhapPF[t]/(KdhapPFvALD*Vpf) + f16bpPF[t]/(Kf16bpPFvALD*Vpf) + gapPF[t]/(KgapPFvALD*Vpf) + (dhapPF[t]*gapPF[t])/(KdhapPFvALD*KgapPFvALD*Vpf^2))), vPFvATPASE -> (VPFvATPASE*atpPF[t]^5)/(KmPFvATPASE^5*Vpf^4*(1 + atpPF[t]^5/(KmPFvATPASE^5*Vpf^5))), vPFvENO -> (VPFvENO*p2gPF[t]*(1 - pepPF[t]/(KeqPFvENO*p2gPF[t])))/(Kp2gPFvENO*(1 + p2gPF[t]/(Kp2gPFvENO*Vpf) + pepPF[t]/(KpepPFvENO*Vpf))), vPFvG3PDH -> (VfPFvG3PDH*dhapPF[t]*nadhPF[t]*(1 - (g3pPF[t]*nadPF[t])/(KeqPFvG3PDH*dhapPF[t]*nadhPF[t])))/(KdhapPFvG3PDH*KnadhPFvG3PDH*Vpf*(1 + dhapPF[t]/(KdhapPFvG3PDH*Vpf) + g3pPF[t]/(Kg3pPFvG3PDH*Vpf))*(1 + nadhPF[t]/(KnadhPFvG3PDH*Vpf) + nadPF[t]/(KnadPFvG3PDH*Vpf))), vPFvGAPDH -> (-((VrPFvGAPDH*b13pgPF[t]*nadhPF[t])/(Kb13pgPFvGAPDH*KnadhPFvGAPDH*Vpf)) + (VPFvGAPDH*gapPF[t]*nadPF[t])/(KgapPFvGAPDH*KnadPFvGAPDH*Vpf))/((1 + b13pgPF[t]/(Kb13pgPFvGAPDH*Vpf) + gapPF[t]/(KgapPFvGAPDH*Vpf))*(1 + nadhPF[t]/(KnadhPFvGAPDH*Vpf) + nadPF[t]/(KnadPFvGAPDH*Vpf))), vPFvGLCtr -> (Vpf*VPFvGLCtr*(glcEX[t]/Vex - glcPF[t]/Vpf))/(KmPFvGLCtr*(1 + glcEX[t]/(KmPFvGLCtr*Vex) + glcPF[t]/(KmPFvGLCtr*Vpf) + (alphaPFvGLCtr*glcEX[t]*glcPF[t])/(KmPFvGLCtr^2*Vex*Vpf))), vPFvGLYtr -> kPFvGLYtr*Vpf*(g3pPF[t]/Vpf - glyEX[t]/Vex), vPFvHK -> (VPFvHK*atpPF[t]*(1 - (adpPF[t]*g6pPF[t])/(KeqPFvHK*atpPF[t]*glcPF[t]))*glcPF[t])/(KatpPFvHK*KglcPFvHK*Vpf*(1 + adpPF[t]/(KadpPFvHK*Vpf) + atpPF[t]/(KatpPFvHK*Vpf))*(1 + atpPF[t]/(KiatpPFvHK*Vpf))*(1 + g6pPF[t]/(Kg6pPFvHK*Vpf) + glcPF[t]/(KglcPFvHK*Vpf))), vPFvLACtr -> KdPFvLACtr*(1 - (hEX*Vpf*lacEX[t])/(hPF*Vex*lacPF[t]))*lacPF[t] + (VPFvLACtr*(1 - (hEX*Vpf*lacEX[t])/(hPF*Vex*lacPF[t]))*lacPF[t])/(KlacPFvLACtr*(1 + lacEX[t]/(KlacPFvLACtr*Vex) + lacPF[t]/(KlacPFvLACtr*Vpf) + pyrEX[t]/(KipyrPFvLACtr*Vex) + pyrPF[t]/(KipyrPFvLACtr*Vpf))), vPFvLDH -> (-((VrPFvLDH*lacPF[t]*nadPF[t])/(KlacPFvLDH*KnadPFvLDH*Vpf)) + (VfPFvLDH*nadhPF[t]*pyrPF[t])/(KnadhPFvLDH*KpyrPFvLDH*Vpf))/((1 + nadhPF[t]/(KnadhPFvLDH*Vpf) + nadPF[t]/(KnadPFvLDH*Vpf))*(1 + lacPF[t]/(KlacPFvLDH*Vpf) + pyrPF[t]/(KpyrPFvLDH*Vpf))), vPFvPFK -> (VPFvPFK*atpPF[t]*f6pPF[t])/(KatpPFvPFK*Kf6pPFvPFK*Vpf*(1 + atpPF[t]/(KatpPFvPFK*Vpf))*(1 + adpPF[t]/(KadpPFvPFK*Vpf) + atpPF[t]/(KatpPFvPFK*Vpf))*(1 + f16bpPF[t]/(Kf16bpPFvPFK*Vpf) + f6pPF[t]/(Kf6pPFvPFK*Vpf))), vPFvPGI -> (VPFvPGI*(1 - f6pPF[t]/(KeqPFvPGI*g6pPF[t]))*g6pPF[t])/(Kg6pPFvPGI*(1 + f6pPF[t]/(Kf6pPFvPGI*Vpf) + g6pPF[t]/(Kg6pPFvPGI*Vpf))), vPFvPGK -> (KadpPFvPGK*Kb13pgPFvPGK*KeqPFvPGK*VrPFvPGK*atpPF[t]*(-1 + (KeqPFvPGK*adpPF[t]*b13pgPF[t])/(atpPF[t]*p3gPF[t]))*p3gPF[t])/(KatpPFvPGK^2*Kp3gPFvPGK^2*Vpf*(1 + adpPF[t]/(KadpPFvPGK*Vpf) + atpPF[t]/(KatpPFvPGK*Vpf))*(1 + b13pgPF[t]/(Kb13pgPFvPGK*Vpf) + p3gPF[t]/(Kp3gPFvPGK*Vpf))), vPFvPGM -> (VPFvPGM*(1 - p2gPF[t]/(KeqPFvPGM*p3gPF[t]))*p3gPF[t])/(Kp3gPFvPGM*(1 + p2gPF[t]/(Kp2gPFvPGM*Vpf) + p3gPF[t]/(Kp3gPFvPGM*Vpf))), vPFvPK -> (VPFvPK*adpPF[t]*pepPF[t])/(KadpPFvPK*KpepPFvPK*Vpf*(1 + adpPF[t]/(KadpPFvPK*Vpf))*(1 + pepPF[t]/(KpepPFvPK*Vpf))*(1 + LPFvPK*(1 + (adpPF[t]/(KiadpPFvPK*Vpf) + atpPF[t]/(KiatpPFvPK*Vpf))^h)*(1 + (pepPF[t]/(KipepPFvPK*Vpf) + pyrPF[t]/(KipyrPFvPK*Vpf))^h))), vPFvPYRtr -> KdPFvPYRtr*(1 - (hEX*Vpf*pyrEX[t])/(hPF*Vex*pyrPF[t]))*pyrPF[t] + (VPFvPYRtr*(1 - (hEX*Vpf*pyrEX[t])/(hPF*Vex*pyrPF[t]))*pyrPF[t])/(KpyrPFvPYRtr*(1 + lacEX[t]/(KilacPFvPYRtr*Vex) + lacPF[t]/(KilacPFvPYRtr*Vpf) + pyrEX[t]/(KpyrPFvPYRtr*Vex) + pyrPF[t]/(KpyrPFvPYRtr*Vpf))), vPFvTPI -> (VPFvTPI*dhapPF[t]*(1 - gapPF[t]/(KeqPFvTPI*dhapPF[t])))/(KdhapPFvTPI*(1 + dhapPF[t]/(KdhapPFvTPI*Vpf) + gapPF[t]/(KgapPFvTPI*Vpf) + pepPF[t]/(KipepPFvTPI*Vpf))) }; parameters = { ConcAdpPF -> 0.0015, ConcAtpPF -> 0.0015, ConcB13pgPF -> 0.0001, ConcDhapPF -> 0.0001, ConcF16bpPF -> 0.0001, ConcF6pPF -> 0.0001, ConcG6pPF -> 0.0001, ConcGapPF -> 0.0001, ConcGlcEX -> 0.005, ConcGlcPF -> 0.0001, ConcGly3pPF -> 0.0001, ConcGlyEX -> 3.79121*^-11, ConcLacEX -> 3.79121*^-11, ConcLacPF -> 0.0001, ConcNadPF -> 0.0015, ConcNadhPF -> 0.0015, ConcP2gPF -> 0.0001, ConcP3gPF -> 0.0001, ConcPepPF -> 1*^-05, ConcPyrEX -> 3.79121*^-11, ConcPyrPF -> 0.0001, KadpPFvHK -> 0.000846735, KadpPFvPFK -> 0.00074176, KadpPFvPGK -> 0.00015, KadpPFvPK -> 0.000317, KatpPFvHK -> 0.00069647, KatpPFvPFK -> 0.0007862, KatpPFvPGK -> 0.00077, Kb13pgPFvGAPDH -> 2.359*^-05, Kb13pgPFvPGK -> 1.34*^-05, KdPFvLACtr -> 0.005, KdPFvPYRtr -> 0.0007, KdhapPFvALD -> 0.00011, KdhapPFvG3PDH -> 0.00034, KdhapPFvTPI -> 0.001954, KeqPFvALD -> 9*^-05, KeqPFvENO -> 4.6, KeqPFvG3PDH -> 32600.0, KeqPFvHK -> 1310.0, KeqPFvPGI -> 0.33, KeqPFvPGK -> 3200.0, KeqPFvPGM -> 0.19, KeqPFvTPI -> 0.04545, Kf16bpPFvALD -> 6.84*^-05, Kf16bpPFvPFK -> 0.003626, Kf6pPFvPFK -> 0.00109454, Kf6pPFvPGI -> 9.6651*^-05, Kg3pPFvG3PDH -> 0.00398, Kg6pPFvHK -> 4.3*^-05, Kg6pPFvPGI -> 0.00100774, KgapPFvALD -> 4.6*^-05, KgapPFvGAPDH -> 0.000917, KgapPFvTPI -> 0.000337, KglcPFvHK -> 0.000168613, KiadpPFvPK -> 0.002, KiatpPFvHK -> 0.026, KiatpPFvPK -> 0.00182, KilacPFvPYRtr -> 0.000358, KipepPFvPK -> 0.00292, KipepPFvTPI -> 1.59*^-05, KipyrPFvLACtr -> 0.00163, KipyrPFvPK -> 0.105, KlacPFvLACtr -> 0.0038, KlacPFvLDH -> 0.003611, KmPFvATPASE -> 0.0045, KmPFvGLCtr -> 0.000213, KnadPFvG3PDH -> 0.00051, KnadPFvGAPDH -> 0.0005662, KnadPFvLDH -> 0.000234, KnadhPFvG3PDH -> 9*^-05, KnadhPFvGAPDH -> 2.87*^-05, KnadhPFvLDH -> 4.6*^-05, Kp2gPFvENO -> 0.000521, Kp2gPFvPGM -> 0.000318, Kp3gPFvPGK -> 0.000267, Kp3gPFvPGM -> 0.00173, KpepPFvENO -> 0.00129, KpepPFvPK -> 0.000406, KpyrPFvLDH -> 0.000133, KpyrPFvPYRtr -> 0.0157, LPFvPK -> 0.255, VPFvALD -> 0.0569593147718, VPFvATPASE -> 0.345, VPFvENO -> 0.286295503195, VPFvGAPDH -> 0.656263383259, VPFvGLCtr -> 0.0469, VPFvHK -> 0.083, VPFvLACtr -> 0.598, VPFvPFK -> 0.41, VPFvPGI -> 0.800428265477, VPFvPGM -> 0.186937901488, VPFvPK -> 0.762, VPFvPYRtr -> 0.216, VPFvTPI -> 1.50599571726, VfPFvG3PDH -> 0.012, VfPFvLDH -> 0.542612419668, VrPFvGAPDH -> 0.243199143455, VrPFvLDH -> 0.290792291203, VrPFvPGK -> 0.353533190557, alphaPFvGLCtr -> 0.91, h -> 4.0, kPFvGLYtr -> 2.0, pHConversionFactor -> 1.0, phEX -> 7.1, phPF -> 7.2, Vex -> 2637.68, Vpf -> 28.0 }; assignments = { hPF -> pHConversionFactor/10^phPF, hEX -> pHConversionFactor/10^phEX }; events = { }; speciesAnnotations = { adpPF[t]->"http://identifiers.org/pubchem.substance/3310", adpPF[t]->"http://identifiers.org/kegg.compound/C00008", adpPF[t]->"http://identifiers.org/3dmet/B01130", atpPF[t]->"http://identifiers.org/pubchem.substance/3304", atpPF[t]->"http://identifiers.org/kegg.compound/C00002", atpPF[t]->"http://identifiers.org/3dmet/B01125", atpPF[t]->"http://identifiers.org/cas/56-65-5", dhapPF[t]->"http://identifiers.org/pubchem.substance/3411", dhapPF[t]->"http://identifiers.org/kegg.compound/C00111", dhapPF[t]->"http://identifiers.org/3dmet/B00029", f16bpPF[t]->"http://identifiers.org/pubchem.substance/3647", f16bpPF[t]->"http://identifiers.org/kegg.compound/C00354", f16bpPF[t]->"http://identifiers.org/3dmet/B04673", f16bpPF[t]->"http://identifiers.org/cas/488-69-7", f6pPF[t]->"http://identifiers.org/kegg.compound/C02976", f6pPF[t]->"http://identifiers.org/pubchem.substance/5887", g3pPF[t]->"http://identifiers.org/3dmet/B01157", g3pPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A15978", g3pPF[t]->"http://identifiers.org/kegg.compound/C00093", g3pPF[t]->"http://identifiers.org/pubchem.substance/3393", g6pPF[t]->"http://identifiers.org/cas/56-73-5", g6pPF[t]->"http://identifiers.org/3dmet/B04630", g6pPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A4170", g6pPF[t]->"http://identifiers.org/kegg.compound/C00092", g6pPF[t]->"http://identifiers.org/pubchem.substance/3392", gapPF[t]->"http://identifiers.org/cas/591-57-1", gapPF[t]->"http://identifiers.org/3dmet/B01163", gapPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A29052", gapPF[t]->"http://identifiers.org/kegg.compound/C00118", gapPF[t]->"http://identifiers.org/pubchem.substance/3418", glcEX[t]->"http://identifiers.org/obo.chebi/CHEBI%3A17634", glcPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A17634", glyEX[t]->"http://identifiers.org/cas/56-81-5", glyEX[t]->"http://identifiers.org/3dmet/B00032", glyEX[t]->"http://identifiers.org/obo.chebi/CHEBI%3A17754", glyEX[t]->"http://identifiers.org/kegg.compound/C00116", glyEX[t]->"http://identifiers.org/pubchem.substance/3416", lacEX[t]->"http://identifiers.org/cas/50-21-5", lacEX[t]->"http://identifiers.org/obo.chebi/CHEBI%3A28358", lacEX[t]->"http://identifiers.org/pubchem.substance/4615", lacEX[t]->"http://identifiers.org/kegg.compound/C01432", lacPF[t]->"http://identifiers.org/cas/50-21-5", lacPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A28358", lacPF[t]->"http://identifiers.org/pubchem.substance/4615", lacPF[t]->"http://identifiers.org/kegg.compound/C01432", nadPF[t]->"http://identifiers.org/3dmet/B01126", nadPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A15846", nadPF[t]->"http://identifiers.org/kegg.compound/C00003", nadPF[t]->"http://identifiers.org/pubchem.substance/3305", nadPF[t]->"http://identifiers.org/cas/53-84-9", nadhPF[t]->"http://identifiers.org/cas/58-68-4", nadhPF[t]->"http://identifiers.org/3dmet/B01127", nadhPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A16908", nadhPF[t]->"http://identifiers.org/kegg.compound/C00004", nadhPF[t]->"http://identifiers.org/pubchem.substance/3306", p2gPF[t]->"http://identifiers.org/3dmet/B01295", p2gPF[t]->"http://identifiers.org/kegg.compound/C00631", p2gPF[t]->"http://identifiers.org/pubchem.substance/3904", p2gPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A17835", p3gPF[t]->"http://identifiers.org/3dmet/B01185", p3gPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A17794", p3gPF[t]->"http://identifiers.org/kegg.compound/C00197", p3gPF[t]->"http://identifiers.org/pubchem.substance/3497", pepPF[t]->"http://identifiers.org/cas/138-08-9", pepPF[t]->"http://identifiers.org/3dmet/B00019", pepPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A44897", pepPF[t]->"http://identifiers.org/kegg.compound/C00074", pepPF[t]->"http://identifiers.org/pubchem.substance/3374", pyrEX[t]->"http://identifiers.org/cas/127-17-3", pyrEX[t]->"http://identifiers.org/3dmet/B00006", pyrEX[t]->"http://identifiers.org/obo.chebi/CHEBI%3A32816", pyrEX[t]->"http://identifiers.org/kegg.compound/C00022", pyrEX[t]->"http://identifiers.org/pubchem.substance/3324", pyrPF[t]->"http://identifiers.org/cas/127-17-3", pyrPF[t]->"http://identifiers.org/3dmet/B00006", pyrPF[t]->"http://identifiers.org/obo.chebi/CHEBI%3A32816", pyrPF[t]->"http://identifiers.org/kegg.compound/C00022", pyrPF[t]->"http://identifiers.org/pubchem.substance/3324" }; reactionAnnotations = { vPFvALD->"http://identifiers.org/ec-code/4.1.2.13", vPFvENO->"http://identifiers.org/ec-code/4.2.1.11", vPFvHK->"http://identifiers.org/ec-code/2.7.1.1" }; units = { {"time" -> "min", "metabolite" -> "fmol/trophozoite", "extent" -> "fmol/trophozoite"} }; (* Time evolution *) odes = { adpPF'[t] == 1.0*vPFvATPASE +1.0*vPFvPFK +1.0*vPFvHK -1.0*vPFvPGK -1.0*vPFvPK, atpPF'[t] == 1.0*vPFvPGK +1.0*vPFvPK -1.0*vPFvATPASE -1.0*vPFvPFK -1.0*vPFvHK, b13pgPF'[t] == 1.0*vPFvGAPDH -1.0*vPFvPGK, dhapPF'[t] == 1.0*vPFvALD -1.0*vPFvG3PDH -1.0*vPFvTPI, f16bpPF'[t] == 1.0*vPFvPFK -1.0*vPFvALD, f6pPF'[t] == 1.0*vPFvPGI -1.0*vPFvPFK, g3pPF'[t] == 1.0*vPFvG3PDH -1.0*vPFvGLYtr, g6pPF'[t] == 1.0*vPFvHK -1.0*vPFvPGI, gapPF'[t] == 1.0*vPFvALD +1.0*vPFvTPI -1.0*vPFvGAPDH, glcEX'[t] == -1.0*vPFvGLCtr, glcPF'[t] == 1.0*vPFvGLCtr -1.0*vPFvHK, glyEX'[t] == 1.0*vPFvGLYtr , lacEX'[t] == 1.0*vPFvLACtr , lacPF'[t] == 1.0*vPFvLDH -1.0*vPFvLACtr, nadPF'[t] == 1.0*vPFvG3PDH +1.0*vPFvLDH -1.0*vPFvGAPDH, nadhPF'[t] == 1.0*vPFvGAPDH -1.0*vPFvG3PDH -1.0*vPFvLDH, p2gPF'[t] == 1.0*vPFvPGM -1.0*vPFvENO, p3gPF'[t] == 1.0*vPFvPGK -1.0*vPFvPGM, pepPF'[t] == 1.0*vPFvENO -1.0*vPFvPK, pyrEX'[t] == 1.0*vPFvPYRtr , pyrPF'[t] == 1.0*vPFvPK -1.0*vPFvLDH -1.0*vPFvPYRtr }; timeCourse = NDSolve[Join[odes, initialValues]//.rateEquations//.assignments//.parameters, variables, {t, 0, 100}]; (* Steady-state solution initialized with result of time evolution *) findRootEquations = odes /.D[_[t],t]->0; findRootVariables = Partition[Flatten[{#, #/.timeCourse/.t->100} &/@variables],2]; steadyStateVariables = FindRoot[findRootEquations//.rateEquations//.assignments//.parameters, findRootVariables, MaxIterations->100] fluxes = #//.assignments//.parameters/.steadyStateVariables&/@rateEquations (* Plot the time evolution of the variables *) plotTable=Table[Plot[variables[[i]]/.parameters/.timeCourse,{t,0,100},PlotLegends->variables[[i]],PlotRange->Full],{i,Length[variables]}]