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curien2

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curien2

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000212) Biomodels notes: Reproduction of figure 7c of the original publication using Copasi 4.6. Steady states were calculated over a range of values for the maximal velocity of tRNA synthetase, V_max_AA_RS using the parameter scan task of Copasi (250 intervals from 0.15 to 2 uM/s). As steady state fluxes in the protein branches, the fluxes through the Lys, Thr, and Ile tRNA synthetase reactions were taken.

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Manuscript information

Understanding the regulation of aspartate metabolism using a model based on measured kinetic parameters.

  • Gilles Curien
  • Olivier Bastien
  • Mylène Robert-Genthon
  • Athel Cornish-Bowden
  • María Luz Cárdenas
  • Renaud Dumas
Mol. Syst. Biol. 2009; 5 : 271
Abstract
The aspartate-derived amino-acid pathway from plants is well suited for analysing the function of the allosteric network of interactions in branched pathways. For this purpose, a detailed kinetic model of the system in the plant model Arabidopsis was constructed on the basis of in vitro kinetic measurements. The data, assembled into a mathematical model, reproduce in vivo measurements and also provide non-intuitive predictions. A crucial result is the identification of allosteric interactions whose function is not to couple demand and supply but to maintain a high independence between fluxes in competing pathways. In addition, the model shows that enzyme isoforms are not functionally redundant, because they contribute unequally to the flux and its regulation. Another result is the identification of the threonine concentration as the most sensitive variable in the system, suggesting a regulatory role for threonine at a higher level of integration.

Unit definitions 9

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
— 1e-06 mole
— 1.0 second^(-1.0)
— 1.0 litre^(-1.0)
— 1e-06 mole litre^(-1.0)
— 1e-06 mole litre^(-1.0) second^(-1.0)
— 1e-12 mole^(2.0) litre^(-2.0)
— 1000000.0 litre mole^(-1.0) second^(-1.0)
— 1e-06 mole second^(-1.0)
— 1.0 dimensionless

Compartments 1

Id Name Spatial dimensions Size
c1 chl 3.0 1.0

Species 31

Id Name Initial quantity Compartment Fixed
AK1 AK1 0.25 c1 (chl) ✔
AK2 AK2 0.25 c1 (chl) ✔
AKHSDHI AKI-HSDHI 0.63 c1 (chl) ✔
AKHSDHII AKII-HSDHII 0.63 c1 (chl) ✔
ASA Aspartate semialdehyde 0.0 c1 (chl) ✘
ASADH ASADH 11.6 c1 (chl) ✔
AdoMet S-adenosyl-methionine 20.0 c1 (chl) ✔
Asp Aspartate 1500.0 c1 (chl) ✔
AspP Aspartyl_P 0.0 c1 (chl) ✘
CGS CGS 0.7 c1 (chl) ✔
Cys Cysteine 15.0 c1 (chl) ✔
Cysta Cystathione 0.0 c1 (chl) ✔
DHDPS1 DHDPS1 1.6 c1 (chl) ✔
DHDPS2 DHDPS2 1.6 c1 (chl) ✔
Gly Glycine 0.0 c1 (chl) ✔
HSK HSK 4.0 c1 (chl) ✔
Hser Homoserine 0.0 c1 (chl) ✘
Ile Isoleucine 0.0 c1 (chl) ✘
IleTRNA Ile-tRNA 0.0 c1 (chl) ✔
LKR LKR 0.0 c1 (chl) ✔
Lys Lysine 0.0 c1 (chl) ✘
LysTRNA Lys-tRNA 0.0 c1 (chl) ✔
PHser Phosphohomoserine 0.0 c1 (chl) ✘
Phosphate — 10000.0 c1 (chl) ✔
Sacc Saccharopine 0.0 c1 (chl) ✔
TD TD 0.36 c1 (chl) ✔
THA THA 0.0 c1 (chl) ✔
TS1 TS1 7.4 c1 (chl) ✘
Thr Threonine 0.0 c1 (chl) ✘
ThrTRNA Thr-tRNA 0.0 c1 (chl) ✔
Val Valine 100.0 c1 (chl) ✔

Initial assignments 0

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
Reactions 18
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
Vak1 Aspartate kinase 1 react. Asp = AspP

c1 * AK1 * ((AK1_kforward_app_exp - AK1_kreverse_app_exp * AspP) / (1 + pow(Lys / (AK1_Lys_Ki_app_exp / (1 + AdoMet / AK1_AdoMet_Ka_app_exp)), AK1_nH_exp)))
Vak2 Aspartate kinase 2 react. Asp = AspP

c1 * AK2 * ((AK2_kforward_app_exp - AK2_kreverse_app_exp * AspP) / (1 + pow(Lys / AK2_Lys_Ki_app_exp, AK2_nH_exp)))
VakI aspartate kinase react. (AKI-HSDHI) Asp = AspP

c1 * AKHSDHI * ((AKI_kforward_app_exp - AKI_kreverse_app_exp * AspP) / (1 + pow(Thr / AKI_Thr_Ki_app_exp, AKI_nH_exp)))
VakII aspartate kinase react. (AKII-HSDHII) Asp = AspP

c1 * AKHSDHII * ((AKII_kforward_app_exp - AKII_kreverse_app_exp * AspP) / (1 + pow(Thr / AKII_Thr_Ki_app_exp, AKII_nH_exp)))
Vasadh Aspartate semialdehyde dehydrogenase react. AspP = ASA

c1 * ASADH * (ASADH_kforward_app_exp * AspP - ASADH_kreverse_app_exp * ASA)
Vcgs Cystathionine gamma synthase react. PHser > Cysta

c1 * CGS * PHser * (CGS_kcat_exp / (1 + CGS_Cys_Km_exp / Cys) / (CGS_Phser_Km_exp / (1 + CGS_Cys_Km_exp / Cys) * (1 + Phosphate / CGS_Phosphate_Ki_exp) + PHser))
Vdhdps1 DHDPS1 react. ASA > Lys

c1 * DHDPS1_k_app_exp * DHDPS1 * ASA * (1 / (1 + pow(Lys / DHDPS1_Lys_Ki_app_exp, DHDPS1_nH_exp)))
Vdhdps2 DHDPS2 react. ASA > Lys

c1 * DHDPS2_k_app_exp * DHDPS2 * ASA * (1 / (1 + pow(Lys / DHDPS2_Lys_Ki_app_exp, DHDPS2_nH_exp)))
Vhsdh1 homoserine dehydrogenase react. (AKI-HSDHI) ASA = Hser

c1 * HSDHI_kforward_app_exp * AKHSDHI * ASA * (HSDHI_Thr_relative_residual_activity_app_exp + HSDHI_Thr_relative_inhibition_app_exp / (1 + Thr / HSDHI_Thr_Ki_app_exp))
Vhsdh2 homoserine dehydrogenase react. (AKII-HSDHII) ASA = Hser

c1 * HSDHII_kforward_app_exp * AKHSDHII * ASA * (HSDHII_Thr_relative_residual_activity_app_exp + HSDHII_Thr_relative_inhibition_app_exp / (1 + Thr / HSDHII_Thr_Ki_app_exp))
Vhsk homoserine kinase react. Hser > PHser

c1 * HSK_kcat_app_exp * HSK * Hser / (HSK_Hser_app_exp + Hser)
VileTRNA Ile aminoacyl tRNA synthetase react. Ile > IleTRNA

c1 * V_Ile_RS * Ile / (Ile_tRNAS_Ile_Km + Ile)
VlysKR Lys ketoglutarate reductase react. Lys > Sacc

c1 * LKR_kcat_exp * LKR * Lys / (LKR_Lys_Km_exp + Lys)
VlysTRNA Lys aminoacyl tRNA synthetase react. Lys > LysTRNA

c1 * V_Lys_RS * Lys / (Lys_tRNAS_Lys_Km + Lys)
Vtd Threonine deaminase react. Thr > Ile

c1 * TD * Thr * (TD_k_app_exp / (1 + pow(Ile / (TD_Ile_Ki_no_Val_app_exp + TD_Val_Ka1_app_exp * Val / (TD_Val_Ka2_app_exp + Val)), TD_nH_app_exp)))
Vtha Thr aldolase react. Thr > Gly

c1 * THA_kcat_exp * THA * Thr / (THA_Thr_Km_exp + Thr)
VthrTRNA Thr aminoacyl tRNA synthetase react. Thr > ThrTRNA

c1 * V_Thr_RS * Thr / (Thr_tRNAS_Thr_Km + Thr)
Vts1 Threonine synthase react. (TS1) PHser > Thr

c1 * TS1 * PHser * ((TS1_kcatmin_exp + TS1_AdoMet_kcatmax_exp * (pow(AdoMet, TS1_nH_exp) / TS1_AdoMet_Ka1_exp)) / (1 + pow(AdoMet, TS1_nH_exp) / TS1_AdoMet_Ka1_exp) / (TS1_AdoMEt_Km_no_AdoMet_exp * ((1 + AdoMet / TS1_AdoMet_Ka2_exp) / (1 + AdoMet / TS1_AdoMet_Ka3_exp) / (1 + pow(AdoMet, TS1_nH_exp) / TS1_AdoMet_Ka4_exp)) * (1 + Phosphate / TS1_Phosphate_Ki_exp) + PHser))

Parameters 60   4

Global parameters

Id Value
V_AA_RS 0.43 umole_per_litre_per_time
V_Ile_RS <assignment rule> umole_per_litre_per_time
V_Lys_RS <assignment rule> umole_per_litre_per_time
V_Thr_RS <assignment rule> umole_per_litre_per_time

Local parameters

Id Value Reaction
AK1_kforward_app_exp 5.65 per_time Vak1 (Aspartate kinase 1 react.)
AK1_kreverse_app_exp 1.6 litre_per_umole_per_time Vak1 (Aspartate kinase 1 react.)
AK1_Lys_Ki_app_exp 550.0 umole_per_litre Vak1 (Aspartate kinase 1 react.)
AK1_AdoMet_Ka_app_exp 3.5 umole_per_litre Vak1 (Aspartate kinase 1 react.)
AK1_nH_exp 2.0 dimensionless Vak1 (Aspartate kinase 1 react.)
AK2_kforward_app_exp 3.15 per_time Vak2 (Aspartate kinase 2 react.)
AK2_kreverse_app_exp 0.86 litre_per_umole_per_time Vak2 (Aspartate kinase 2 react.)
AK2_Lys_Ki_app_exp 22.0 umole_per_litre Vak2 (Aspartate kinase 2 react.)
AK2_nH_exp 1.1 dimensionless Vak2 (Aspartate kinase 2 react.)
AKI_kforward_app_exp 0.36 per_time VakI (aspartate kinase react. (AKI-HSDHI))
AKI_kreverse_app_exp 0.15 litre_per_umole_per_time VakI (aspartate kinase react. (AKI-HSDHI))
AKI_Thr_Ki_app_exp 124.0 umole_per_litre VakI (aspartate kinase react. (AKI-HSDHI))
AKI_nH_exp 2.0 dimensionless VakI (aspartate kinase react. (AKI-HSDHI))
AKII_kforward_app_exp 1.35 per_time VakII (aspartate kinase react. (AKII-HSDHII))
AKII_kreverse_app_exp 0.22 litre_per_umole_per_time VakII (aspartate kinase react. (AKII-HSDHII))
AKII_Thr_Ki_app_exp 109.0 umole_per_litre VakII (aspartate kinase react. (AKII-HSDHII))
AKII_nH_exp 2.0 dimensionless VakII (aspartate kinase react. (AKII-HSDHII))
ASADH_kforward_app_exp 0.9 litre_per_umole_per_time Vasadh (Aspartate semialdehyde dehydrogenase react.)
ASADH_kreverse_app_exp 0.23 litre_per_umole_per_time Vasadh (Aspartate semialdehyde dehydrogenase react.)
DHDPS1_k_app_exp 1.0 umole_per_litre Vdhdps1 (DHDPS1 react.)
DHDPS1_Lys_Ki_app_exp 10.0 umole_per_litre Vdhdps1 (DHDPS1 react.)
DHDPS1_nH_exp 2.0 dimensionless Vdhdps1 (DHDPS1 react.)
DHDPS2_k_app_exp 1.0 umole_per_litre Vdhdps2 (DHDPS2 react.)
DHDPS2_Lys_Ki_app_exp 33.0 umole_per_litre Vdhdps2 (DHDPS2 react.)
DHDPS2_nH_exp 2.0 dimensionless Vdhdps2 (DHDPS2 react.)
HSDHI_kforward_app_exp 0.84 litre_per_umole_per_time Vhsdh1 (homoserine dehydrogenase react. (AKI-HSDHI))
HSDHI_Thr_relative_residual_activity_app_exp 0.14 dimensionless Vhsdh1 (homoserine dehydrogenase react. (AKI-HSDHI))
HSDHI_Thr_relative_inhibition_app_exp 0.86 dimensionless Vhsdh1 (homoserine dehydrogenase react. (AKI-HSDHI))
HSDHI_Thr_Ki_app_exp 400.0 umole_per_litre Vhsdh1 (homoserine dehydrogenase react. (AKI-HSDHI))
HSDHII_kforward_app_exp 0.64 litre_per_umole_per_time Vhsdh2 (homoserine dehydrogenase react. (AKII-HSDHII))
HSDHII_Thr_relative_residual_activity_app_exp 0.25 dimensionless Vhsdh2 (homoserine dehydrogenase react. (AKII-HSDHII))
HSDHII_Thr_relative_inhibition_app_exp 0.75 dimensionless Vhsdh2 (homoserine dehydrogenase react. (AKII-HSDHII))
HSDHII_Thr_Ki_app_exp 8500.0 umole_per_litre Vhsdh2 (homoserine dehydrogenase react. (AKII-HSDHII))
HSK_kcat_app_exp 2.8 per_time Vhsk (homoserine kinase react.)
HSK_Hser_app_exp 14.0 umole_per_litre Vhsk (homoserine kinase react.)
TS1_kcatmin_exp 0.42 dimensionless Vts1 (Threonine synthase react. (TS1))
TS1_AdoMet_kcatmax_exp 3.5 dimensionless Vts1 (Threonine synthase react. (TS1))
TS1_AdoMet_Ka1_exp 73.0 umole2_per_litre2 Vts1 (Threonine synthase react. (TS1))
TS1_nH_exp 2.0 dimensionless Vts1 (Threonine synthase react. (TS1))
TS1_Phosphate_Ki_exp 1000.0 umole_per_litre Vts1 (Threonine synthase react. (TS1))
TS1_AdoMEt_Km_no_AdoMet_exp 250.0 dimensionless Vts1 (Threonine synthase react. (TS1))
TS1_AdoMet_Ka2_exp 0.5 dimensionless Vts1 (Threonine synthase react. (TS1))
TS1_AdoMet_Ka3_exp 1.09 dimensionless Vts1 (Threonine synthase react. (TS1))
TS1_AdoMet_Ka4_exp 140.0 umole2_per_litre2 Vts1 (Threonine synthase react. (TS1))
CGS_kcat_exp 30.0 dimensionless Vcgs (Cystathionine gamma synthase react.)
CGS_Cys_Km_exp 460.0 dimensionless Vcgs (Cystathionine gamma synthase react.)
CGS_Phser_Km_exp 2500.0 dimensionless Vcgs (Cystathionine gamma synthase react.)
CGS_Phosphate_Ki_exp 2000.0 dimensionless Vcgs (Cystathionine gamma synthase react.)
TD_k_app_exp 0.0124 dimensionless Vtd (Threonine deaminase react.)
TD_Ile_Ki_no_Val_app_exp 30.0 dimensionless Vtd (Threonine deaminase react.)
TD_Val_Ka1_app_exp 73.0 dimensionless Vtd (Threonine deaminase react.)
TD_Val_Ka2_app_exp 615.0 umole_per_litre Vtd (Threonine deaminase react.)
TD_nH_app_exp 3.0 dimensionless Vtd (Threonine deaminase react.)
Lys_tRNAS_Lys_Km 25.0 umole_per_litre VlysTRNA (Lys aminoacyl tRNA synthetase react.)
Thr_tRNAS_Thr_Km 100.0 umole_per_litre VthrTRNA (Thr aminoacyl tRNA synthetase react.)
Ile_tRNAS_Ile_Km 20.0 umole_per_litre VileTRNA (Ile aminoacyl tRNA synthetase react.)
LKR_kcat_exp 3.1 per_time VlysKR (Lys ketoglutarate reductase react.)
LKR_Lys_Km_exp 13000.0 umole_per_litre VlysKR (Lys ketoglutarate reductase react.)
THA_kcat_exp 1.7 per_time Vtha (Thr aldolase react.)
THA_Thr_Km_exp 7100.0 umole_per_litre Vtha (Thr aldolase react.)

Rules 0   0   3

Assignment rules

Definition
V_Ile_RS = V_AA_RS
V_Thr_RS = V_AA_RS
V_Lys_RS = V_AA_RS

Rate rules

Definition

Algebraic rules

Definition

Events 0

Trigger Assignments