/* * Glycolysis in bloodstream form Trypanosoma brucei can be understood * in terms of the kinetics of the glycolytic enzymes * * Model Status * * This model is valid CellML and appears to match the published * equations. However the model will not run in either COR or OpenCell. * * Model Structure * * ABSTRACT: In trypanosomes the first part of glycolysis takes * place in specialized microbodies, the glycosomes. Most glycolytic * enzymes of Trypanosoma brucei have been purified and characterized * kinetically. In this paper a mathematical model of glycolysis * in the bloodstream form of this organism is developed on the * basis of all available kinetic data. The fluxes and the cytosolic * metabolite concentrations as predicted by the model were in * accordance with available data as measured in non-growing trypanosomes, * both under aerobic and under anaerobic conditions. The model * also reproduced the inhibition of anaerobic glycolysis by glycerol, * although the amount of glycerol needed to inhibit glycolysis * completely was lower than experimentally determined. At low * extracellular glucose concentrations the intracellular glucose * concentration remained very low, and only at 5 mM of extracellular * glucose, free glucose started to accumulate intracellularly, * in close agreement with experimental observations. This biphasic * relation could be related to the large difference between the * affinities of the glucose transporter and hexokinase for intracellular * glucose. The calculated intraglycosomal metabolite concentrations * demonstrated that enzymes that have been shown to be near-equilibrium * in the cytosol must work far from equilibrium in the glycosome * in order to maintain the high glycolytic flux in the latter. * * The original paper reference is cited below: * * Glycolysis in Bloodstream Form Trypanosoma brucei Can Be Understood * in Terms of the Kinetics of the Glycolytic Enzyme, Barbara M. * Bakker, Paul A. M. Michels, Fred R. Opperdoes, and Hans V. Westerhoff, * 1997, The Journal of Biological Chemistry , 272, 3207-3215. * PubMed ID: 9013556 * * A reaction diagram of glycolysis * * [[Image file: bakker_1997.png]] * * The stoichiometric scheme of the model of glycolysis in the * bloodstream form of the parasite Trypanosoma brucei. */ import nsrunit; unit conversion on; unit minute=60 second^1; // unit micromolar predefined // unit millimolar predefined // unit nanomolar predefined unit flux=1.6666667E-8 meter^(-3)*second^(-1)*mole^1; math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real Vc_Vg dimensionless; Vc_Vg=22.3; real Glc_o millimolar; Glc_o=5.0; real Glc_i(time) millimolar; when(time=time.min) Glc_i=0.01; real V_HK(time) flux; real V_glucose_transport(time) flux; real Glc_6_P_g(time) millimolar; real Keq_PGI dimensionless; Keq_PGI=0.29; real Fru_6_P_g(time) millimolar; real hexose_P_g(time) millimolar; when(time=time.min) hexose_P_g=0.01; real V_PFK(time) flux; real Fru_1_6_BP_g(time) millimolar; when(time=time.min) Fru_1_6_BP_g=0.01; real V_ALD(time) flux; real GA_3_P_g(time) millimolar; real Keq_TIM dimensionless; Keq_TIM=0.045; real DHAP_g(time) millimolar; real triose_P(time) millimolar; when(time=time.min) triose_P=0.01; real V_GAPDH(time) flux; real V_GDH(time) flux; real V_GPO(time) flux; real one_three_BPGA_g(time) millimolar; when(time=time.min) one_three_BPGA_g=0.01; real V_PGK(time) flux; real three_PGA(time) millimolar; real N(time) millimolar; when(time=time.min) N=0.01; real Keq_PGM dimensionless; Keq_PGM=0.187; real Keq_ENO dimensionless; Keq_ENO=6.7; real two_PGA_c(time) millimolar; real V_PYK(time) flux; real PEP_c(time) millimolar; real PYR_c(time) millimolar; when(time=time.min) PYR_c=0.01; real V_pyruvate_transport(time) flux; real glycerol_g millimolar; glycerol_g=0.00; real DHAP(time) millimolar; real DHAP_c(time) millimolar; real Gly_3_P(time) millimolar; real ATP_g(time) millimolar; real ADP_g(time) millimolar; real C4 millimolar; C4=120.0; real Gly_3_P_c(time) millimolar; real Gly_3_P_g(time) millimolar; real NAD_g(time) millimolar; real NADH_g(time) millimolar; when(time=time.min) NADH_g=0.01; real C3 millimolar; C3=4.0; real P_g(time) millimolar; when(time=time.min) P_g=0.01; real V_GK(time) flux; real P_c(time) millimolar; when(time=time.min) P_c=0.01; real V_ATP_utilisation(time) flux; real ATP_g.Keq_AK dimensionless; ATP_g.Keq_AK=0.442; real C1 millimolar; C1=3.9; real ATP_c(time) millimolar; real ATP_c.Keq_AK dimensionless; ATP_c.Keq_AK=0.442; real C2 millimolar; C2=3.9; real ADP_c(time) millimolar; real AMP_g(time) millimolar; real AMP_c(time) millimolar; real K_Glc millimolar; K_Glc=2.0; real alpha dimensionless; alpha=0.75; real V_glucose_transport_max flux; V_glucose_transport_max=106.2; real K_pyruvate millimolar; K_pyruvate=1.96; real V_pyruvate_transport_max flux; V_pyruvate_transport_max=160.0; real V_GPO.K_Gly_3_P millimolar; V_GPO.K_Gly_3_P=1.7; real V_GPO_max flux; V_GPO_max=200.0; real K_Glc_i millimolar; K_Glc_i=0.1; real V_HK.K_ATP millimolar; V_HK.K_ATP=0.116; real V_HK.K_ADP millimolar; V_HK.K_ADP=0.126; real V_HK_max flux; V_HK_max=625.0; real V_GAPDH.K_NAD millimolar; V_GAPDH.K_NAD=0.45; real K_GA_3_P millimolar; K_GA_3_P=0.15; real V_GAPDH.K_1_3_BPGA millimolar; V_GAPDH.K_1_3_BPGA=0.1; real V_GAPDH.K_NADH millimolar; V_GAPDH.K_NADH=0.02; real V_GAPDH_max_plus flux; V_GAPDH_max_plus=1470.0; real V_GAPDH_max_ratio dimensionless; V_GAPDH_max_ratio=0.67; real V_PGK.K_ADP millimolar; V_PGK.K_ADP=0.1; real V_PGK.K_1_3_BPGA millimolar; V_PGK.K_1_3_BPGA=0.05; real K_3_PGA millimolar; K_3_PGA=1.62; real V_PGK.K_ATP millimolar; V_PGK.K_ATP=0.29; real V_PGK_max_plus flux; V_PGK_max_plus=640.0; real V_PGK_max_ratio dimensionless; V_PGK_max_ratio=0.029; real V_GK.K_ADP millimolar; V_GK.K_ADP=0.12; real V_GK.K_Gly_3_P millimolar; V_GK.K_Gly_3_P=5.1; real K_glycerol millimolar; K_glycerol=0.12; real V_GK.K_ATP millimolar; V_GK.K_ATP=0.19; real V_GK_max_plus flux; V_GK_max_plus=0.0; real V_GK_max_ratio dimensionless; V_GK_max_ratio=167.0; real V_GDH.K_NADH millimolar; V_GDH.K_NADH=0.01; real V_GDH.K_Gly_3_P millimolar; V_GDH.K_Gly_3_P=2.0; real K_DHAP millimolar; K_DHAP=0.1; real V_GDH.K_NAD millimolar; V_GDH.K_NAD=0.4; real V_GDH_max_plus flux; V_GDH_max_plus=533.0; real V_GDH_max_ratio dimensionless; V_GDH_max_ratio=0.28; real V_PFK.n dimensionless; V_PFK.n=1.2; real Km_Fru_6_P millimolar; Km_Fru_6_P=0.82; real Km_ATP millimolar; Km_ATP=2.6E-2; real V_PFK_max flux; V_PFK_max=780.0; real Km_PEP(time) millimolar; real Km_ADP millimolar; Km_ADP=0.114; real V_PYK.n dimensionless; V_PYK.n=2.5; real V_PYK_max flux; V_PYK_max=2.6E3; real Km_Fru_1_6_BP(time) millimolar; real Km_GA_3_P millimolar; Km_GA_3_P=6.7E-2; real Ki_GA_3_P millimolar; Ki_GA_3_P=9.8E-2; real Km_DHAP millimolar; Km_DHAP=1.5E-2; real V_ALD_max_plus flux; V_ALD_max_plus=780.0; real V_ALD_max_ratio dimensionless; V_ALD_max_ratio=1.19; real k flux; k=50; // // // // Glc_i:time=(V_glucose_transport-V_HK); // Glc_6_P_g=(hexose_P_g/Keq_PGI); // Fru_6_P_g=(hexose_P_g-Glc_6_P_g); // hexose_P_g:time=(V_HK-V_PFK); // Fru_1_6_BP_g:time=(V_PFK-V_ALD); // GA_3_P_g=(Keq_TIM*DHAP_g); // triose_P:time=(2*V_ALD+V_GPO-(V_GAPDH+V_GDH)); // one_three_BPGA_g:time=(V_GAPDH-V_PGK); // three_PGA=(N*(1+Vc_Vg)/(1+(1+Keq_PGM+Keq_PGM*Keq_ENO)*Vc_Vg)); // two_PGA_c=(Keq_PGM*three_PGA); // N:time=(V_PGK-V_PYK); // PEP_c=(Keq_ENO*two_PGA_c); // PYR_c:time=(V_PYK-V_pyruvate_transport); // // DHAP=(triose_P*(1+Vc_Vg)/(1+Vc_Vg+Keq_TIM)); // DHAP_c=DHAP; // DHAP_g=DHAP; // Gly_3_P=((C4-(Glc_6_P_g+Fru_6_P_g+2*Fru_1_6_BP_g+GA_3_P_g+one_three_BPGA_g+2*ATP_g+ADP_g))/(1+Vc_Vg)-DHAP); // Gly_3_P_c=Gly_3_P; // Gly_3_P_g=Gly_3_P; // NAD_g=(C3-NADH_g); // NADH_g:time=(V_GAPDH-V_GDH); // P_g:time=(V_PGK+V_GK-(V_HK+V_PFK)); // P_c:time=(V_PYK-V_ATP_utilisation); // ATP_g=((C1-(-1)*(P_g*(1-4*ATP_g.Keq_AK))+((C1-(-1)*(P_g*(1-4*ATP_g.Keq_AK)))^2-4*(1-4*ATP_g.Keq_AK)*((-1)*ATP_g.Keq_AK*P_g^2))^.5)/(2*(1-4*ATP_g.Keq_AK))); // ATP_c=((C2-(-1)*(P_c*(1-4*ATP_c.Keq_AK))+((C2-(-1)*(P_c*(1-4*ATP_c.Keq_AK)))^2-4*(1-4*ATP_c.Keq_AK)*((-1)*ATP_c.Keq_AK*P_c^2))^.5)/(2*(1-4*ATP_c.Keq_AK))); // ADP_g=(P_g-2*ATP_g); // ADP_c=(P_c-2*ATP_c); // AMP_g=(C1-(ATP_g+ADP_g)); // AMP_c=(C2-(ATP_c+ADP_c)); // // // // // V_glucose_transport=(V_glucose_transport_max*((Glc_o-Glc_i)/(K_Glc+Glc_o+Glc_i+alpha*Glc_o*(Glc_i/K_Glc)))); // V_pyruvate_transport=(V_pyruvate_transport_max*(PYR_c/K_pyruvate)*(1+PYR_c/K_pyruvate)); // V_GPO=(V_GPO_max*(Gly_3_P_c/V_GPO.K_Gly_3_P)*(1+Gly_3_P_c/V_GPO.K_Gly_3_P)); // V_HK=(V_HK_max*(ATP_g/V_HK.K_ATP*(Glc_i/K_Glc_i)/((1+ATP_g/V_HK.K_ATP+ADP_g/V_HK.K_ADP)*(1+Glc_i/K_Glc_i)))); // V_GAPDH=(V_GAPDH_max_plus*(GA_3_P_g/K_GA_3_P*(NAD_g/V_GAPDH.K_NAD-V_GAPDH_max_ratio)*(one_three_BPGA_g/V_GAPDH.K_1_3_BPGA)*(NADH_g/V_GAPDH.K_NADH)/((1+GA_3_P_g/K_GA_3_P+one_three_BPGA_g/V_GAPDH.K_1_3_BPGA)*(1+NAD_g/V_GAPDH.K_NAD+NADH_g/V_GAPDH.K_NADH)))); // V_PGK=(V_PGK_max_plus*(one_three_BPGA_g/V_PGK.K_1_3_BPGA*(ADP_g/V_PGK.K_ADP-V_PGK_max_ratio)*(three_PGA/K_3_PGA)*(ATP_g/V_PGK.K_ATP)/((1+one_three_BPGA_g/V_PGK.K_1_3_BPGA+three_PGA/K_3_PGA)*(1+ADP_g/V_PGK.K_ADP+ATP_g/V_PGK.K_ATP)))); // V_GK=(V_GK_max_plus*(Gly_3_P_g/V_GK.K_Gly_3_P*(ADP_g/V_GK.K_ADP-V_GK_max_ratio)*(glycerol_g/K_glycerol)*(ATP_g/V_GK.K_ATP)/((1+Gly_3_P_g/V_GK.K_Gly_3_P+glycerol_g/K_glycerol)*(1+ADP_g/V_GK.K_ADP+ATP_g/V_GK.K_ATP)))); // V_GDH=(V_GDH_max_plus*(DHAP_g/K_DHAP*(NADH_g/V_GDH.K_NADH-V_GDH_max_ratio)*(Gly_3_P_g/V_GDH.K_Gly_3_P)*(NAD_g/V_GDH.K_NAD)/((1+DHAP_g/K_DHAP+Gly_3_P_g/V_GDH.K_Gly_3_P)*(1+NADH_g/V_GDH.K_NADH+NAD_g/V_GDH.K_NAD)))); // V_PFK=(V_PFK_max*((Fru_6_P_g/Km_Fru_6_P)^V_PFK.n*(ATP_g/Km_ATP)/((1+(Fru_6_P_g/Km_Fru_6_P)^V_PFK.n)*(1+ATP_g/Km_ATP)))); // V_PYK=(V_PYK_max*((PEP_c/Km_PEP)^V_PYK.n*(ADP_c/Km_ADP)/((1+(PEP_c/Km_PEP)^V_PYK.n)*(1+ADP_c/Km_ADP)))); Km_PEP=((.34 millimolar)*(1+ATP_c/(.57 millimolar)+ADP_c/(.64 millimolar))); // V_ALD=(V_ALD_max_plus*((Fru_1_6_BP_g/Km_Fru_1_6_BP-V_ALD_max_ratio*(GA_3_P_g*DHAP_g/(Km_GA_3_P*Km_DHAP)))/(1+Fru_1_6_BP_g/Km_Fru_1_6_BP+GA_3_P_g/Km_GA_3_P+DHAP_g/Km_DHAP+Fru_1_6_BP_g*GA_3_P_g/(Km_Fru_1_6_BP*Ki_GA_3_P)+DHAP_g*GA_3_P_g/(Km_DHAP*Km_GA_3_P)))); Km_Fru_1_6_BP=((.009000000000000001 millimolar)*(1+ATP_g/(.68 millimolar)+ADP_g/(1.51 millimolar)+AMP_g/(3.65 millimolar))); // V_ATP_utilisation=(k*(ATP_c/ADP_c)); }