albert1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000211) Biomodels notes: The model reproduces Figure 5 of the original paper. The model was simulated using Copasi v.4.4.27.

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Experimental and in silico analyses of glycolytic flux control in bloodstream form Trypanosoma brucei.

  • Marie-Astrid Albert
  • Jurgen R Haanstra
  • Véronique Hannaert
  • Joris Van Roy
  • Fred R Opperdoes
  • Barbara M Bakker
  • Paul A M Michels
J. Biol. Chem. 2005; 280 (31): 28306-28315
Abstract
A mathematical model of glycolysis in bloodstream form Trypanosoma brucei was developed previously on the basis of all available enzyme kinetic data (Bakker, B. M., Michels, P. A. M., Opperdoes, F. R., and Westerhoff, H. V. (1997) J. Biol. Chem. 272, 3207-3215). The model predicted correctly the fluxes and cellular metabolite concentrations as measured in non-growing trypanosomes and the major contribution to the flux control exerted by the plasma membrane glucose transporter. Surprisingly, a large overcapacity was predicted for hexokinase (HXK), phosphofructokinase (PFK), and pyruvate kinase (PYK). Here, we present our further analysis of the control of glycolytic flux in bloodstream form T. brucei. First, the model was optimized and extended with recent information about the kinetics of enzymes and their activities as measured in lysates of in vitro cultured growing trypanosomes. Second, the concentrations of five glycolytic enzymes (HXK, PFK, phosphoglycerate mutase, enolase, and PYK) in trypanosomes were changed by RNA interference. The effects of the knockdown of these enzymes on the growth, activities, and levels of various enzymes and glycolytic flux were studied and compared with model predictions. Data thus obtained support the conclusion from the in silico analysis that HXK, PFK, and PYK are in excess, albeit less than predicted. Interestingly, depletion of PFK and enolase had an effect on the activity (but not, or to a lesser extent, expression) of some other glycolytic enzymes. Enzymes located both in the glycosomes (the peroxisome-like organelles harboring the first seven enzymes of the glycolytic pathway of trypanosomes) and in the cytosol were affected. These data suggest the existence of novel regulatory mechanisms operating in trypanosome glycolysis.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1.0 second
0.001 mole
0.001 litre
Id Name Spatial dimensions Size
compartment_1 cytosol 3.0 1.0
compartment_2 glycosome 3.0 1.0
compartment_3 extracellular 3.0 1.0
Id Name Initial quantity Compartment Fixed
species_1 pyruvate 10.0 compartment_1 (cytosol)
species_10 glucose 0.0 compartment_2 (glycosome)
species_11 atpg 0.240501857508 compartment_2 (glycosome)
species_12 adpg 1.51899628498 compartment_2 (glycosome)
species_13 ampg 4.24050185751 compartment_2 (glycosome)
species_14 glucose6phosphate 0.5 compartment_2 (glycosome)
species_15 fructose6phosphate 0.5 compartment_2 (glycosome)
species_16 fructose16bisphosphate 10.0 compartment_2 (glycosome)
species_17 dihydroxyacetonephosphate 8.47911460193 compartment_2 (glycosome)
species_18 glyceraldehyde3phosphate 2.5 compartment_2 (glycosome)
species_19 nad 2.0 compartment_2 (glycosome)
species_2 adpc 1.31652277625 compartment_1 (cytosol)
species_20 nadh 2.0 compartment_2 (glycosome)
species_21 bisphosphoglycerate 0.5 compartment_2 (glycosome)
species_22 glycerol3phosphate 10.5208853981 compartment_2 (glycosome)
species_23 3phosphoglycerate 0.0 compartment_2 (glycosome)
species_24 glycerol 0.0 compartment_2 (glycosome)
species_25 glucose external 5.0 compartment_3 (extracellular)
species_26 pyruvate external 0.0 compartment_3 (extracellular)
species_27 glycerol external 0.0 compartment_3 (extracellular)
species_3 atpc 0.341738611875 compartment_1 (cytosol)
species_4 phosphoenolpyruvate 0.0 compartment_1 (cytosol)
species_5 2phosphoglycerate 0.0 compartment_1 (cytosol)
species_6 ampc 2.24173861188 compartment_1 (cytosol)
species_7 3phosphoglycerate cytosol 0.0 compartment_1 (cytosol)
species_8 dihydroxyacetonephosphate cytosol 2.23134594788 compartment_1 (cytosol)
species_9 glycerol3phosphate cytosol 2.76865405212 compartment_1 (cytosol)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
vAKc adenylate kinase cytosol species_3 + species_6 = {2.0}species_2

compartment_1 * function_22(k, species_3, species_6, keqak, species_2)
vAKg adenylate kinase glycosome species_11 + species_13 = {2.0}species_12

compartment_2 * function_22(k, species_11, species_13, keqak, species_12)
vALD aldolase species_16 = species_17 + species_18

compartment_2 * function_14(Vmax_v5, species_16, species_18, species_17, Keq_v5, species_11, species_12, species_13, r_v5, KGAP_v5, KGAPi_v5)
vANTI gly3p dhap antiporter species_22 + species_8 = species_9 + species_17

k1 * species_22 * species_8 - k2 * species_9 * species_17
vAU atp utilisation species_3 > species_2

compartment_1 * function_20(k, species_3, species_2)
vENO enolase species_5 = species_4

RaENO * compartment_1 * function_12(species_5, species_4, Kms, Kmp, Vf, Vr)
vGAPDH glyceraldehyde3phosphatedehydrogenase species_18 + species_19 = species_21 + species_20

compartment_2 * function_15(Vmax_v7, species_18, KGAP_v7, species_19, KNAD_v7, r_v7, species_21, KBPGA13_v7, species_20, KNADH_v7)
vGK glycerol kinase species_22 + species_12 = species_24 + species_11

compartment_2 * function_21(Vmax_v14, species_22, KGly3Pg_v14, species_12, KADPg_v14, r_v14, species_24, KGlycerol_v14, species_11, KATPg_v14)
vGPDH glycerol3phosphatedehydrogenase species_17 + species_20 = species_19 + species_22

compartment_2 * function_16(Vmax_v8, species_17, KDHAPg_v8, species_20, KNADH_v8, r_v8, species_19, KNAD_v8, species_22, KGly3Pg_v8)
vGPO glycerol3phosphate oxidase species_9 > species_8

compartment_1 * function_17(species_9, Km, V)
vGT glucose transport species_25 = species_10

function_10(Vmax_v1, species_25, species_10, KGlc, Alpha_v1)
vGlyT glycerol transport species_24 = species_27

k1 * species_24 - k2 * species_27
vHK hexokinase species_10 + species_11 = species_14 + species_12

RaHXK * compartment_2 * function_11(Vmax_v2, species_10, KGlcInt_v2, species_11, KATPg_v2, species_12, KADPg_v2, species_14, KGlc6P_v2)
vPFK phophofructokinase species_15 + species_11 = species_16 + species_12

RaPFK * compartment_2 * function_13(Vmax_v4, Ki1Fru16BP_v4, species_16, species_15, KFru6P_v4, species_11, KATPg_v4, Ki2Fru16BP_v4)
vPGI phosphoglycerate isomerase species_14 = species_15

compartment_2 * function_12(species_14, species_15, Kms, Kmp, Vf, Vr)
vPGK phosphoglycerate kinase species_21 + species_12 = species_23 + species_11

compartment_2 * function_18(Vmax_v11, species_21, KBPGA13_v11, species_12, KADPg_v11, r_v11, species_23, KPGA3_v11, species_11, KATPg_v11)
vPGM phosphoglycerate mutase species_7 = species_5

RaPGAM * compartment_1 * function_12(species_7, species_5, Kms, Kmp, Vf, Vr)
vPGT 3phosphoglycerate transport species_23 = species_7

k1 * species_23 - k2 * species_7
vPK pyruvate kinase species_4 + species_2 = species_1 + species_3

RaPYK * compartment_1 * function_19(Vmax_v12, species_4, PK_n, species_2, KADP_v12, species_3)
vPT pyruvate transport species_1 > species_26

function_17(species_1, Km, V)
vTPI triosephosphate isomerase species_17 = species_18

compartment_2 * function_12(species_17, species_18, Kms, Kmp, Vf, Vr)

Global parameters

Id Value
RaENO 1.0
RaHXK 1.0
RaPFK 1.0
RaPGAM 1.0
RaPYK 1.0

Local parameters

Id Value Reaction
KATPg_v2 0.116 vHK (hexokinase)
Vmax_v1 108.9 vGT (glucose transport)
KGlc 1.0 vGT (glucose transport)
Alpha_v1 0.75 vGT (glucose transport)
Vmax_v2 1929.0 vHK (hexokinase)
KGlcInt_v2 0.1 vHK (hexokinase)
KADPg_v2 0.126 vHK (hexokinase)
KGlc6P_v2 12.0 vHK (hexokinase)
Kms 0.4 vPGI (phosphoglycerate isomerase)
Kmp 0.12 vPGI (phosphoglycerate isomerase)
Vf 1305.0 vPGI (phosphoglycerate isomerase)
Vr 1305.0 vPGI (phosphoglycerate isomerase)
Vmax_v4 1708.0 vPFK (phophofructokinase)
Ki1Fru16BP_v4 15.8 vPFK (phophofructokinase)
KFru6P_v4 0.82 vPFK (phophofructokinase)
KATPg_v4 0.026 vPFK (phophofructokinase)
Ki2Fru16BP_v4 10.7 vPFK (phophofructokinase)
Vmax_v5 560.0 vALD (aldolase)
Keq_v5 0.069 vALD (aldolase)
r_v5 1.19 vALD (aldolase)
KGAP_v5 0.067 vALD (aldolase)
KGAPi_v5 0.098 vALD (aldolase)
Kms 1.2 vTPI (triosephosphate isomerase)
Kmp 0.25 vTPI (triosephosphate isomerase)
Vf 999.3 vTPI (triosephosphate isomerase)
Vr 5696.01 vTPI (triosephosphate isomerase)
Vmax_v7 720.9 vGAPDH (glyceraldehyde3phosphatedehydrogenase)
KGAP_v7 0.15 vGAPDH (glyceraldehyde3phosphatedehydrogenase)
KNAD_v7 0.45 vGAPDH (glyceraldehyde3phosphatedehydrogenase)
r_v7 0.67 vGAPDH (glyceraldehyde3phosphatedehydrogenase)
KBPGA13_v7 0.1 vGAPDH (glyceraldehyde3phosphatedehydrogenase)
KNADH_v7 0.02 vGAPDH (glyceraldehyde3phosphatedehydrogenase)
Vmax_v8 465.0 vGPDH (glycerol3phosphatedehydrogenase)
KDHAPg_v8 0.1 vGPDH (glycerol3phosphatedehydrogenase)
KNADH_v8 0.01 vGPDH (glycerol3phosphatedehydrogenase)
r_v8 0.28 vGPDH (glycerol3phosphatedehydrogenase)
KNAD_v8 0.4 vGPDH (glycerol3phosphatedehydrogenase)
KGly3Pg_v8 2.0 vGPDH (glycerol3phosphatedehydrogenase)
Km 1.7 vGPO (glycerol3phosphate oxidase)
V 368.0 vGPO (glycerol3phosphate oxidase)
Km 1.96 vPT (pyruvate transport)
V 200.0 vPT (pyruvate transport)
Vmax_v11 2862.0 vPGK (phosphoglycerate kinase)
KBPGA13_v11 0.003 vPGK (phosphoglycerate kinase)
KADPg_v11 0.1 vPGK (phosphoglycerate kinase)
r_v11 0.47 vPGK (phosphoglycerate kinase)
KPGA3_v11 1.62 vPGK (phosphoglycerate kinase)
KATPg_v11 0.29 vPGK (phosphoglycerate kinase)
Vmax_v12 1020.0 vPK (pyruvate kinase)
PK_n 2.5 vPK (pyruvate kinase)
KADP_v12 0.114 vPK (pyruvate kinase)
k 50.0 vAU (atp utilisation)
Vmax_v14 200.0 vGK (glycerol kinase)
KGly3Pg_v14 3.83 vGK (glycerol kinase)
KADPg_v14 0.56 vGK (glycerol kinase)
r_v14 60.86 vGK (glycerol kinase)
KGlycerol_v14 0.44 vGK (glycerol kinase)
KATPg_v14 0.24 vGK (glycerol kinase)
Kms 0.27 vPGM (phosphoglycerate mutase)
Kmp 0.11 vPGM (phosphoglycerate mutase)
Vf 225.0 vPGM (phosphoglycerate mutase)
Vr 495.0 vPGM (phosphoglycerate mutase)
Kms 0.054 vENO (enolase)
Kmp 0.24 vENO (enolase)
Vf 598.0 vENO (enolase)
Vr 394.68 vENO (enolase)
k 1000000.0 vAKc (adenylate kinase cytosol)
keqak 0.442 vAKc (adenylate kinase cytosol)
k 1000000.0 vAKg (adenylate kinase glycosome)
keqak 0.442 vAKg (adenylate kinase glycosome)
k1 1000000.0 vPGT (3phosphoglycerate transport)
k2 1000000.0 vPGT (3phosphoglycerate transport)
k1 1000000.0 vANTI (gly3p dhap antiporter)
k2 1000000.0 vANTI (gly3p dhap antiporter)
k1 1000000.0 vGlyT (glycerol transport)
k2 1000000.0 vGlyT (glycerol transport)

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Definition
function_17(substrate, Km, V) = V * substrate / (Km + substrate)
function_12(substrate, product, Kms, Kmp, Vf, Vr) = (Vf * substrate / Kms - Vr * product / Kmp) / (1 + substrate / Kms + product / Kmp)
function_20(k, atpc, adpc) = k * atpc / adpc
function_18(Vmax_v11, BPGA13, KBPGA13_v11, ADPg, KADPg_v11, r_v11, PGA3, KPGA3_v11, ATPg, KATPg_v11) = Vmax_v11 * ((BPGA13 / KBPGA13_v11 * (ADPg / KADPg_v11) - r_v11 * (PGA3 / KPGA3_v11) * (ATPg / KATPg_v11)) / ((1 + BPGA13 / KBPGA13_v11 + PGA3 / KPGA3_v11) * (1 + ADPg / KADPg_v11 + ATPg / KATPg_v11)))
function_11(Vmax_v2, GlucoseInt, KGlcInt_v2, ATPg, KATPg_v2, ADPg, KADPg_v2, Glc6P, KGlc6P_v2) = Vmax_v2 * (GlucoseInt / KGlcInt_v2) * (ATPg / KATPg_v2) / ((1 + ATPg / KATPg_v2 + ADPg / KADPg_v2) * (1 + GlucoseInt / KGlcInt_v2 + Glc6P / KGlc6P_v2))
function_22(k, atp, amp, keqak, adp) = k * (atp * amp - keqak * adp * adp)
function_10(Vmax_v1, GlucoseExt, GlucoseInt, KGlc, Alpha_v1) = Vmax_v1 * ((GlucoseExt - GlucoseInt) / (KGlc + GlucoseExt + GlucoseInt + Alpha_v1 * GlucoseExt * GlucoseInt / KGlc))
function_14(Vmax_v5, Fru16BP, GAP, DHAPg, Keq_v5, ATPg, ADPg, AMPg, r_v5, KGAP_v5, KGAPi_v5) = Vmax_v5 * (Fru16BP - GAP * DHAPg / Keq_v5) / (0.009 * (1 + ATPg / 0.68 + ADPg / 1.51 + AMPg / 3.65) + Fru16BP + GAP * (0.015 * (1 + ATPg / 0.68 + ADPg / 1.51 + AMPg / 3.65) / Keq_v5) * (1 / r_v5) + DHAPg * (KGAP_v5 / Keq_v5) * (1 / r_v5) + Fru16BP * GAP / KGAPi_v5 + GAP * DHAPg / Keq_v5 * (1 / r_v5))
function_21(Vmax_v14, Gly3Pg, KGly3Pg_v14, ADPg, KADPg_v14, r_v14, Glycerol, KGlycerol_v14, ATPg, KATPg_v14) = Vmax_v14 * ((Gly3Pg / KGly3Pg_v14 * (ADPg / KADPg_v14) - r_v14 * (Glycerol / KGlycerol_v14) * (ATPg / KATPg_v14)) / ((1 + Gly3Pg / KGly3Pg_v14 + Glycerol / KGlycerol_v14) * (1 + ADPg / KADPg_v14 + ATPg / KATPg_v14)))
function_13(Vmax_v4, Ki1Fru16BP_v4, Fru16BP, Fru6P, KFru6P_v4, ATPg, KATPg_v4, Ki2Fru16BP_v4) = Vmax_v4 * (Ki1Fru16BP_v4 / (Ki1Fru16BP_v4 + Fru16BP)) * (Fru6P / KFru6P_v4) * (ATPg / KATPg_v4) / ((1 + Fru6P / KFru6P_v4 + Fru16BP / Ki2Fru16BP_v4) * (1 + ATPg / KATPg_v4))
function_16(Vmax_v8, DHAPg, KDHAPg_v8, NADH, KNADH_v8, r_v8, NAD, KNAD_v8, Gly3Pg, KGly3Pg_v8) = Vmax_v8 * ((DHAPg / KDHAPg_v8 * (NADH / KNADH_v8) - r_v8 * (NAD / KNAD_v8) * (Gly3Pg / KGly3Pg_v8)) / ((1 + DHAPg / KDHAPg_v8 + Gly3Pg / KGly3Pg_v8) * (1 + NADH / KNADH_v8 + NAD / KNAD_v8)))
function_19(Vmax_v12, PEP, PK_n, ADPc, KADP_v12, ATPc) = Vmax_v12 * pow(PEP / (0.34 * (1 + ATPc / 0.57 + ADPc / 0.64)), PK_n) * (ADPc / KADP_v12) / ((1 + pow(PEP / (0.34 * (1 + ATPc / 0.57 + ADPc / 0.64)), PK_n)) * (1 + ADPc / KADP_v12))
function_15(Vmax_v7, GAP, KGAP_v7, NAD, KNAD_v7, r_v7, BPGA13, KBPGA13_v7, NADH, KNADH_v7) = Vmax_v7 * ((GAP / KGAP_v7 * (NAD / KNAD_v7) - r_v7 * (BPGA13 / KBPGA13_v7) * (NADH / KNADH_v7)) / ((1 + GAP / KGAP_v7 + BPGA13 / KBPGA13_v7) * (1 + NAD / KNAD_v7 + NADH / KNADH_v7)))
Trigger Assignments