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Title

Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: equations and parameter refinement

Authors

Peter J. MULQUINEY and Philip W. KUCHEL

Affiliations

Department of Biochemistry, University of Sydney, Sydney, NSW 2006, Australia

Abstract

Over the last 25 years, several mathematical models of erythrocyte metabolism have been developed. Although these models have identified the key features in the regulation and control of erythrocyte metabolism, many important aspects remain un- explained. In particular, none of these models have satisfactorily accounted for 2,3-bisphosphoglycerate (2,3-BPG) metabolism. 2,3-BPG is an important modulator of haemoglobin oxygen affinity, and hence an understanding of the regulation of 2,3- BPG concentration is important for understanding blood oxygen transport. A detailed, comprehensive, and hence realistic math- ematical model of erythrocyte metabolism is presented that can explain the regulation and control of 2,3-BPG concentration and turnover. The model is restricted to the core metabolic pathways, namely glycolysis, the 2,3-BPG shunt and the pentose phosphate pathway (PPP), and includes membrane transport of metabolites, the binding of metabolites to haemoglobin and Mg5+, as well as pH effects on key enzymic reactions and binding processes. The model is necessarily complex, since it is intended to describe the regulation and control of 2,3-BPG metabolism under a wide variety of physiological and experimental conditions. In addition, since H+ and blood oxygen tension are important external effectors of 2,3-BPG concentration, it was important that the model take into account the large array of kinetic and binding phenomena that result from changes in these effectors. Through an iterative loop of experimental and simulation analysis many values of enzyme-kinetic parameters of the model were refined to yield close conformity between model simulations and ‘ real ’ experimental data. This iterative process enabled a single set of parameters to be found which described well the metabolic behaviour of the erythrocyte under a wide variety of conditions.

Journal

Biochem. J. (1999) 342, 581–596

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 mole
1.0 mole litre^(-1.0)
1.0 second
1.0 litre
Id Name Spatial dimensions Size
compartment compartment 3.0 1.0 L
Id Name Initial quantity Compartment Fixed
ADP ADP 0.00031 mole/L compartment (compartment)
AMP AMP 3e-05 mole/L compartment (compartment)
ATP ATP 0.0021 mole/L compartment (compartment)
B13PG B13PG 7e-07 mole/L compartment (compartment)
B23PG B23PG 0.0067 mole/L compartment (compartment)
BPGSP BPGSP 3.8e-06 mole/L compartment (compartment)
BPGSPB13PG BPGSPB13PG 0.0 mole/L compartment (compartment)
BPGSPB23PG BPGSPB23PG 0.0 mole/L compartment (compartment)
BPGSPP BPGSPP 0.0 mole/L compartment (compartment)
BPGSPPP2GA BPGSPPP2GA 0.0 mole/L compartment (compartment)
BPGSPPP3GA BPGSPPP3GA 0.0 mole/L compartment (compartment)
BPGSPPPhos BPGSPPPhos 0.0 mole/L compartment (compartment)
CO2 CO2 0.0012 mole/L compartment (compartment)
Ery4P Ery4P 1e-05 mole/L compartment (compartment)
Fru16P2 Fru16P2 2.7e-06 mole/L compartment (compartment)
Fru6P Fru6P 1.3e-05 mole/L compartment (compartment)
GSH GSH 0.0032 mole/L compartment (compartment)
GSSG GSSG 9e-08 mole/L compartment (compartment)
Glc Glc 0.005 mole/L compartment (compartment)
Glc16P2 Glc16P2 0.000122 mole/L compartment (compartment)
Glc6P Glc6P 4e-05 mole/L compartment (compartment)
GraP GraP 5.7e-06 mole/L compartment (compartment)
GrnP GrnP 1.9e-05 mole/L compartment (compartment)
Hb Hb 0.007 mole/L compartment (compartment)
HbADP HbADP 0.0 mole/L compartment (compartment)
HbATP HbATP 0.0 mole/L compartment (compartment)
HbB13PG HbB13PG 0.0 mole/L compartment (compartment)
HbB23PG HbB23PG 0.0 mole/L compartment (compartment)
HbMgATP HbMgATP 0.0 mole/L compartment (compartment)
Lac Lac 0.0014 mole/L compartment (compartment)
Lace Lace 0.00182 mole/L compartment (compartment)
Mg Mg 0.003 mole/L compartment (compartment)
MgADP MgADP 0.0 mole/L compartment (compartment)
MgATP MgATP 0.0 mole/L compartment (compartment)
MgB13PG MgB13PG 0.0 mole/L compartment (compartment)
MgB23PG MgB23PG 0.0 mole/L compartment (compartment)
MgFru16P2 MgFru16P2 0.0 mole/L compartment (compartment)
MgGlc16P2 MgGlc16P2 0.0 mole/L compartment (compartment)
MgPhos MgPhos 0.0 mole/L compartment (compartment)
NAD NAD 6e-05 mole/L compartment (compartment)
NADH NADH 1.4e-07 mole/L compartment (compartment)
NADP NADP 1.25e-07 mole/L compartment (compartment)
NADPH NADPH 6.4e-05 mole/L compartment (compartment)
P2GA P2GA 1e-05 mole/L compartment (compartment)
P3GA P3GA 6.4e-05 mole/L compartment (compartment)
P6G P6G 1.4e-07 mole/L compartment (compartment)
P6GL P6GL 1.4e-10 mole/L compartment (compartment)
PEP PEP 2.3e-05 mole/L compartment (compartment)
Phos Phos 0.001 mole/L compartment (compartment)
Phose Phose 0.00192 mole/L compartment (compartment)
Pyr Pyr 6e-05 mole/L compartment (compartment)
Pyre Pyre 8.5e-05 mole/L compartment (compartment)
Rib5P Rib5P 1e-05 mole/L compartment (compartment)
Ru5P Ru5P 1e-05 mole/L compartment (compartment)
Sed7P Sed7P 1e-05 mole/L compartment (compartment)
TK TK 3.3e-07 mole/L compartment (compartment)
TKG TKG 0.0 mole/L compartment (compartment)
TKGEry4P TKGEry4P 0.0 mole/L compartment (compartment)
TKGRib5P TKGRib5P 0.0 mole/L compartment (compartment)
TKXu5P TKXu5P 0.0 mole/L compartment (compartment)
Xu5P Xu5P 1e-06 mole/L compartment (compartment)

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
vak vak MgADP + ADP = MgATP + AMP

4300 * (1 + Khadp / pow(10, pH1) + Kkadp * k1) * ADP * MgADP - 1400 * (1 + Khamp / pow(10, pH1) + Kkamp * k1) * AMP * MgATP
vald vald Fru16P2 = GrnP + GraP

VALD * (Fru16P2 * kcatfald / Kmaldfru16p2 - GraP * GrnP * kcatrald / (Kialdgrnp * Kmaldgrap)) / (1 + GrnP / Kialdgrnp + Fru16P2 / Kmaldfru16p2 + GraP * GrnP / (Kialdgrnp * Kmaldgrap) + Fru16P2 * GraP * Kmaldgrnp / (Kialdfru16p2 * Kialdgrnp * Kmaldgrap) + (B23PG + MgB23PG) / Kialdb23pg + GraP * Kmaldgrnp * (1 + (B23PG + MgB23PG) / Kialdb23pg) / (Kialdgrnp * Kmaldgrap))
vatpase vatpase MgATP = MgADP + Phos

katpase * MgATP
vbpgsp1 vbpgsp1 B13PG + BPGSP = BPGSPB13PG

2.80950914520767 * pow(10, 8) * B13PG * BPGSP / (1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1)) - kbpgsp2 * BPGSPB13PG
vbpgsp2 vbpgsp2 BPGSPB13PG = BPGSPP + P3GA

17.4099179927889 * BPGSPB13PG / (1 + 4.78630092322638 * pow(10, 28) / pow(10, 4 * pH1))
vbpgsp3 vbpgsp3 BPGSPP + P3GA = BPGSPPP3GA

-kbpgsp5 * BPGSPPP3GA + 3.25336851380399 * pow(10, 8) * BPGSPP * P3GA / (1 + 4.78630092322638 * pow(10, 28) / pow(10, 4 * pH1))
vbpgsp4 vbpgsp4 BPGSPP + P2GA = BPGSPPP2GA

-kbpgsp7 * BPGSPPP2GA + 1758.57757502918 * BPGSPP * P2GA / (1 + 4.78630092322638 * pow(10, 28) / pow(10, 4 * pH1))
vbpgsp5 vbpgsp5 BPGSPPP3GA = BPGSPB23PG

kbpgsp8 * BPGSPPP3GA - kbpgsp9 * BPGSPB23PG
vbpgsp6 vbpgsp6 BPGSPPP2GA = BPGSPB23PG

kbpgsp10 * BPGSPPP2GA - kbpgsp11 * BPGSPB23PG
vbpgsp7 vbpgsp7 BPGSPB23PG = BPGSP + B23PG

-(6.32139557671725 * pow(10, 6) * B23PG * BPGSP / (1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1))) + kbpgsp12 * BPGSPB23PG
vbpgsp8 vbpgsp8 BPGSPP + Phos = BPGSPPPhos

kbpgsp14 * BPGSPP * Phos - kbpgsp15 * BPGSPPPhos
vbpgsp9 vbpgsp9 BPGSPPPhos = BPGSP + {2.0}Phos

kbpgsp16 * BPGSPPPhos
veno veno P2GA = PEP

VENO * (kcatfeno * Mg * P2GA / (Kienomg * Kmenop2ga) - kcatreno * Mg * PEP / (Kienopep * Kmenomg)) / (1 + Mg / Kienomg + P2GA / Kienop2ga + Mg * P2GA / (Kienomg * Kmenop2ga) + PEP / Kienopep + Mg * PEP / (Kienopep * Kmenomg))
vg6pdh vg6pdh Glc6P + NADP = P6GL + NADPH

VG6PDH * (Glc6P * kg6pdh1 * kg6pdh3 * kg6pdh5 * kg6pdh7 * kg6pdh9 * NADP - kg6pdh2 * kg6pdh4 * kg6pdh6 * kg6pdh8 * kg6pdh10 * NADPH * P6GL) / (Glc6P * kg6pdh3 * kg6pdh5 * kg6pdh7 * kg6pdh9 + kg6pdh2 * (kg6pdh4 * kg6pdh6 + kg6pdh4 * kg6pdh7 + kg6pdh5 * kg6pdh7) * kg6pdh9 + kg6pdh1 * (kg6pdh4 * kg6pdh6 + kg6pdh4 * kg6pdh7 + kg6pdh5 * kg6pdh7) * kg6pdh9 * NADP + Glc6P * kg6pdh1 * kg6pdh3 * (kg6pdh5 * kg6pdh7 + kg6pdh5 * kg6pdh9 + kg6pdh6 * kg6pdh9 + kg6pdh7 * kg6pdh9) * NADP + Glc6P * kg6pdh3 * kg6pdh5 * kg6pdh7 * kg6pdh10 * NADPH + kg6pdh2 * (kg6pdh4 * kg6pdh6 + kg6pdh5 * kg6pdh6 + kg6pdh5 * kg6pdh7) * kg6pdh10 * NADPH + kg6pdh2 * kg6pdh4 * kg6pdh6 * kg6pdh8 * P6GL + kg6pdh1 * kg6pdh4 * kg6pdh6 * kg6pdh8 * NADP * P6GL + Glc6P * kg6pdh1 * kg6pdh3 * (kg6pdh5 + kg6pdh6) * kg6pdh8 * NADP * P6GL + Glc6P * kg6pdh3 * (kg6pdh5 + kg6pdh6) * kg6pdh8 * kg6pdh10 * NADPH * P6GL + (kg6pdh2 * kg6pdh4 + kg6pdh2 * kg6pdh5 + kg6pdh2 * kg6pdh6 + kg6pdh4 * kg6pdh6) * kg6pdh8 * kg6pdh10 * NADPH * P6GL)
vgapdh vgapdh GraP + Phos + NAD = B13PG + NADH

VGDH * (-5.40304497429925 * pow(10, 35) * B13PG * NADH / pow(10, pH1) + 1.45911949685535 * pow(10, 21) * GraP * NAD * Phos / (Kigapdhphos * Kmgapdhnad)) / (2.19517763377412 * pow(10, 20) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * B13PG * (1 + GraP / Kidgapdhgrap) + 2.0985345932935 * pow(10, 18) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * GraP * (1 + GraP / Kidgapdhgrap) + 1 / Kigapdhnad * 2.19517763377412 * pow(10, 20) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * B13PG * NAD + 1 / Kigapdhnad * 2.0985345932935 * pow(10, 18) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * GraP * NAD + 1.05427942060955 * pow(10, 33) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * Kmgapdhb13pg * NADH / pow(10, pH1) + 1.05427942060955 * pow(10, 33) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * B13PG * NADH / pow(10, pH1) + 3.32595319105503 * pow(10, 30) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * GraP * NADH / pow(10, pH1) + 1 / Kigapdhphos * 2.0985345932935 * pow(10, 18) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * GraP * (1 + GraP / Kidgapdhgrap) * Phos + 2.0985345932935 * pow(10, 18) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * Kmgapdhgrap * NAD * Phos / (Kigapdhphos * Kmgapdhnad) + 2.0985345932935 * pow(10, 18) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * Kmgapdhgrap * B13PG * NAD * Phos / (Kidgapdhb13pg * Kigapdhphos * Kmgapdhnad) + 2.0985345932935 * pow(10, 18) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * GraP * NAD * Phos / (Kigapdhphos * Kmgapdhnad) + 1 / Kigapdhphos * (1.05427942060955 * pow(10, 33) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * Kmgapdhb13pg * NADH * Phos / pow(10, pH1)) + 1.05427942060955 * pow(10, 33) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * Kmgapdhb13pg * B13PG * NADH * Phos / pow(10, pH1) / (Kidgapdhb13pg * Kigapdhphos) + 1 / Kigapdhphos * (3.32595319105503 * pow(10, 30) * (1 + 3.16227766016838 * pow(10, 7) / pow(10, pH1) + 1 * pow(10, -10) * pow(10, pH1)) * GraP * NADH * Phos / pow(10, pH1)))
vgpi vgpi Glc6P = Fru6P

VGPI * (-(Fru6P * kcatrgpi / Kmgpifru6p) + Glc6P * kcatfgpi / Kmgpiglc6p) / (1 + Fru6P / Kmgpifru6p + Glc6P / Kmgpiglc6p)
vgssgr vgssgr NADPH + GSSG = NADP + {2.0}GSH

VGSSGR * (-(GSH^2) * kgssgr2 * kgssgr4 * kgssgr6 * kgssgr8 * kgssgr10 * kgssgr12 * NADP + GSSG * kgssgr1 * kgssgr3 * kgssgr5 * kgssgr7 * kgssgr9 * kgssgr11 * NADPH) / (GSH^2 * kgssgr2 * kgssgr4 * kgssgr6 * kgssgr8 * kgssgr10 + GSH * kgssgr2 * kgssgr4 * kgssgr6 * kgssgr8 * kgssgr11 + GSSG * kgssgr3 * kgssgr5 * kgssgr7 * kgssgr9 * kgssgr11 + kgssgr2 * (kgssgr4 * kgssgr6 + kgssgr4 * kgssgr7 + kgssgr5 * kgssgr7) * kgssgr9 * kgssgr11 + GSH * kgssgr2 * kgssgr4 * kgssgr6 * kgssgr8 * kgssgr12 * NADP + GSSG * kgssgr3 * kgssgr5 * kgssgr7 * kgssgr9 * kgssgr12 * NADP + kgssgr2 * (kgssgr4 * kgssgr6 + kgssgr4 * kgssgr7 + kgssgr5 * kgssgr7) * kgssgr9 * kgssgr12 * NADP + GSH * GSSG * kgssgr3 * kgssgr5 * kgssgr7 * kgssgr10 * kgssgr12 * NADP + GSH * kgssgr2 * (kgssgr4 * kgssgr6 + kgssgr4 * kgssgr7 + kgssgr5 * kgssgr7) * kgssgr10 * kgssgr12 * NADP + GSH^2 * GSSG * kgssgr3 * (kgssgr5 + kgssgr6) * kgssgr8 * kgssgr10 * kgssgr12 * NADP + GSH^2 * (kgssgr2 * kgssgr4 + kgssgr2 * kgssgr5 + kgssgr2 * kgssgr6 + kgssgr4 * kgssgr6) * kgssgr8 * kgssgr10 * kgssgr12 * NADP + GSH * GSSG * kgssgr1 * kgssgr3 * kgssgr5 * kgssgr7 * kgssgr10 * NADPH + GSH^2 * kgssgr1 * kgssgr4 * kgssgr6 * kgssgr8 * kgssgr10 * NADPH + GSH^2 * GSSG * kgssgr1 * kgssgr3 * (kgssgr5 + kgssgr6) * kgssgr8 * kgssgr10 * NADPH + GSH * kgssgr1 * kgssgr4 * kgssgr6 * kgssgr8 * kgssgr11 * NADPH + GSH * GSSG * kgssgr1 * kgssgr3 * (kgssgr5 + kgssgr6) * kgssgr8 * kgssgr11 * NADPH + kgssgr1 * (kgssgr4 * kgssgr6 + kgssgr4 * kgssgr7 + kgssgr5 * kgssgr7) * kgssgr9 * kgssgr11 * NADPH + GSSG * kgssgr1 * kgssgr3 * (kgssgr5 * kgssgr7 * kgssgr9 + kgssgr5 * kgssgr7 * kgssgr11 + kgssgr5 * kgssgr9 * kgssgr11 + kgssgr6 * kgssgr9 * kgssgr11 + kgssgr7 * kgssgr9 * kgssgr11) * NADPH)
vhbadp vhbadp Hb + ADP = HbADP

-HbADP * khbadpd + 300000 * ADP * Hb * (1 + 3.16978638492223 * pow(10, 7) * Kahb + 2.51188643150958 * pow(10, 14) * pow(Kahb, 2)) / (1 + pow(2, 1 + pH1) * pow(5, pH1) * Kahb + pow(10, 2 * pH1) * pow(Kahb, 2))
vhbatp vhbatp Hb + ATP = HbATP

-HbATP * khbatpd + 432000 * ATP * Hb * (1 + 3.16978638492223 * pow(10, 7) * Kahb + 2.51188643150958 * pow(10, 14) * pow(Kahb, 2)) / (1 + pow(2, 1 + pH1) * pow(5, pH1) * Kahb + pow(10, 2 * pH1) * pow(Kahb, 2))
vhbb13pg vhbb13pg Hb + B13PG = HbB13PG

-HbB13PG * khbb13pgd + 380000 * B13PG * Hb * (1 + 3.16978638492223 * pow(10, 7) * Kahb + 2.51188643150958 * pow(10, 14) * pow(Kahb, 2)) / (1 + pow(2, 1 + pH1) * pow(5, pH1) * Kahb + pow(10, 2 * pH1) * pow(Kahb, 2))
vhbbpg vhbbpg Hb + B23PG = HbB23PG

-HbB23PG * khbbpgd + 300000 * B23PG * Hb * (1 + 3.16978638492223 * pow(10, 7) * Kahb + 2.51188643150958 * pow(10, 14) * pow(Kahb, 2)) / (1 + pow(2, 1 + pH1) * pow(5, pH1) * Kahb + pow(10, 2 * pH1) * pow(Kahb, 2))
vhbmgatp vhbmgatp Hb + MgATP = HbMgATP

-HbMgATP * khbmgatpd + 46800 * Hb * (1 + 3.16978638492223 * pow(10, 7) * Kahb + 2.51188643150958 * pow(10, 14) * pow(Kahb, 2)) * MgATP / (1 + pow(2, 1 + pH1) * pow(5, pH1) * Kahb + pow(10, 2 * pH1) * pow(Kahb, 2))
vhk vhk Glc + MgATP = MgADP + Glc6P

2.85714 * VHK * Vi * (-(1.92792 * Glc6P * MgADP / ((1 + 1.0471285480509 * pow(10, 7) / pow(10, pH1) + 2.81838293126445 * pow(10, -10) * pow(10, pH1)) * Kihkglc6p * Kmhkmgadp)) + 299.16 * Glc * MgATP / ((1 + 1.0471285480509 * pow(10, 7) / pow(10, pH1) + 2.81838293126445 * pow(10, -10) * pow(10, pH1)) * Kihkglc * Kmhkmgatp)) / (1 + Glc / Kihkglc + Glc * B23PG / (Kdihkbpg * Kihkglc) + Glc * Glc16P2 / (Kdihkglc16p2 * Kihkglc) + Glc * Glc6P / (Kdihkglc6p * Kihkglc) + Glc6P / Kihkglc6p + Glc * GSH / (Kdihkgsh * Kihkglc) + MgADP / Kihkmgadp + Glc6P * MgADP / (Kihkglc6p * Kmhkmgadp) + MgATP / Kihkmgatp + Glc * MgATP / (Kihkglc * Kmhkmgatp))
vlactransport vlactransport Lac = Lace

2.85714 * (-klactransporti * Lace * Ve + klactransporti * Ve * Lac / (1 + pow(10, -3.73 + pH1)) * (1 + pow(10, -3.73 + pH1) / rtv))
vldh vldh Pyr + NADH = Lac + NAD

VLDH * (-(1306.64221547056 * kcatrldh * Lac * NAD / ((1 + 6.30957344480193 * pow(10, 6) / pow(10, pH1)) * Kildhnad)) + 25634.207529267 * kcatfldh * NADH * Pyr / ((1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1)) * Kildhnadh)) / (NAD / Kildhnad + 1306.64221547056 * Lac * NAD / ((1 + 6.30957344480193 * pow(10, 6) / pow(10, pH1)) * Kildhnad) + NADH / Kildhnadh + 1306.64221547056 * Kmldhnad * Lac * NADH / ((1 + 6.30957344480193 * pow(10, 6) / pow(10, pH1)) * Kildhnad * Kildhnadh) + 25634.207529267 * Kmldhnadh * NAD * Pyr / ((1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1)) * Kildhnad * Kildhnadh) + 2.01262239795994 * pow(10, 7) * Lac * NAD * Pyr / ((1 + 6.30957344480193 * pow(10, 6) / pow(10, pH1)) * (1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1)) * Kildhnad) + 25634.207529267 * NADH * Pyr / ((1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1)) * Kildhnadh) + 4.88940918937581 * pow(10, 6) * Lac * NADH * Pyr / ((1 + 6.30957344480193 * pow(10, 6) / pow(10, pH1)) * (1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1)) * Kildhnadh) + (1 + Pyr / Kidldhpyr) * (1 + 1306.64221547056 * Kmldhnad * Lac / ((1 + 6.30957344480193 * pow(10, 6) / pow(10, pH1)) * Kildhnad) + 25634.207529267 * Kmldhnadh * Pyr / ((1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1)) * Kildhnadh)))
vldhp vldhp Pyr + NADPH = Lac + NADP

(-(krldhp * Lac * NADP / Kmldhplac) + kfldhp * NADPH * Pyr / Kmldhppyr) / (1 + Lac / Kmldhplac + Pyr / Kmldhppyr)
vmgadp vmgadp Mg + ADP = MgADP

1711.2 * ADP * (Kmgadp + Khadp * Kmghadp / pow(10, pH1)) * Mg / (1 + Khadp / pow(10, pH1) + k1 * Kkadp) - kmgadpd * MgADP
vmgatp vmgatp ATP + Mg = MgATP

2620.8 * ATP * (Kmgatp + Khatp * Kmghatp / pow(10, pH1)) * Mg / (1 + Khatp / pow(10, pH1) + k1 * Kkatp) - kmgatpd * MgATP
vmgb13pg vmgb13pg Mg + B13PG = MgB13PG

729.6 * B13PG * (Kmgbpg + Khbpg * Kmghbpg / pow(10, pH1)) * Mg / (1 + Khbpg / pow(10, pH1) + Kh2bpg * Khbpg / pow(10, 2 * pH1) + k1 * Kkbpg + k1 * Khbpg * Kkhbpg / pow(10, pH1)) - kmgb13pgd * MgB13PG
vmgb23pg vmgb23pg Mg + B23PG = MgB23PG

2572.8 * B23PG * (Kmgbpg + Khbpg * Kmghbpg / pow(10, pH1)) * Mg / (1 + Khbpg / pow(10, pH1) + Kh2bpg * Khbpg / pow(10, 2 * pH1) + k1 * Kkbpg + k1 * Khbpg * Kkhbpg / pow(10, pH1)) - kmgbpgd * MgB23PG
vmgfru16p2 vmgfru16p2 Mg + Fru16P2 = MgFru16P2

3984 * Fru16P2 * (Kmgfru16p2 + Khf * Kmghf / pow(10, pH1)) * Mg / (1 + Khf / pow(10, pH1) + Kh2f * Khf / pow(10, 2 * pH1) + k1 * Kkf + k1 * Khf * Kkhf / pow(10, pH1)) - kmgf16p2d * MgFru16P2
vmgglc16p2 vmgglc16p2 Mg + Glc16P2 = MgGlc16P2

3984 * Glc16P2 * (Kmgfru16p2 + Khf * Kmghf / pow(10, pH1)) * Mg / (1 + Khf / pow(10, pH1) + Kh2f * Khf / pow(10, 2 * pH1) + k1 * Kkf + k1 * Khf * Kkhf / pow(10, pH1)) - kmgf16p2d * MgGlc16P2
vmgphos vmgphos Mg + Phos = MgPhos

-kmgphosd * MgPhos + 40800 * (1 + 6.30957344480193 * pow(10, -8) * Khphos + 0.15 * Kkphos) * Mg * Phos / (1 + Khphos / pow(10, pH1) + k1 * Kkphos)
vox vox {2.0}GSH = GSSG

kox * GSH
voxnadh voxnadh NADH = NAD

koxNADH * NADH
vp6gdh vp6gdh P6G + NADP = CO2 + Ru5P + NADPH

VP6GDH * (kp6gdh1 * kp6gdh3 * kp6gdh5 * kp6gdh7 * kp6gdh9 * kp6gdh11 * NADP * P6G - CO2 * kp6gdh2 * kp6gdh4 * kp6gdh6 * kp6gdh8 * kp6gdh10 * kp6gdh12 * NADPH * Ru5P) / (CO2 * kp6gdh2 * kp6gdh4 * kp6gdh6 * kp6gdh8 * kp6gdh11 + kp6gdh2 * (kp6gdh4 * kp6gdh6 + kp6gdh4 * kp6gdh7 + kp6gdh5 * kp6gdh7) * kp6gdh9 * kp6gdh11 + CO2 * kp6gdh1 * kp6gdh4 * kp6gdh6 * kp6gdh8 * kp6gdh11 * NADP + kp6gdh1 * (kp6gdh4 * kp6gdh6 + kp6gdh4 * kp6gdh7 + kp6gdh5 * kp6gdh7) * kp6gdh9 * kp6gdh11 * NADP + CO2 * kp6gdh2 * kp6gdh4 * kp6gdh6 * kp6gdh8 * kp6gdh12 * NADPH + kp6gdh2 * (kp6gdh4 * kp6gdh6 + kp6gdh4 * kp6gdh7 + kp6gdh5 * kp6gdh7) * kp6gdh9 * kp6gdh12 * NADPH + kp6gdh3 * kp6gdh5 * kp6gdh7 * kp6gdh9 * kp6gdh11 * P6G + CO2 * kp6gdh1 * kp6gdh3 * (kp6gdh5 + kp6gdh6) * kp6gdh8 * kp6gdh11 * NADP * P6G + kp6gdh1 * kp6gdh3 * (kp6gdh5 * kp6gdh7 * kp6gdh9 + kp6gdh5 * kp6gdh7 * kp6gdh11 + kp6gdh5 * kp6gdh9 * kp6gdh11 + kp6gdh6 * kp6gdh9 * kp6gdh11 + kp6gdh7 * kp6gdh9 * kp6gdh11) * NADP * P6G + kp6gdh3 * kp6gdh5 * kp6gdh7 * kp6gdh9 * kp6gdh12 * NADPH * P6G + CO2 * kp6gdh2 * kp6gdh4 * kp6gdh6 * kp6gdh8 * kp6gdh10 * Ru5P + CO2 * kp6gdh1 * kp6gdh4 * kp6gdh6 * kp6gdh8 * kp6gdh10 * NADP * Ru5P + kp6gdh2 * (kp6gdh4 * kp6gdh6 + kp6gdh4 * kp6gdh7 + kp6gdh5 * kp6gdh7) * kp6gdh10 * kp6gdh12 * NADPH * Ru5P + CO2 * (kp6gdh2 * kp6gdh4 + kp6gdh2 * kp6gdh5 + kp6gdh2 * kp6gdh6 + kp6gdh4 * kp6gdh6) * kp6gdh8 * kp6gdh10 * kp6gdh12 * NADPH * Ru5P + kp6gdh1 * kp6gdh3 * kp6gdh5 * kp6gdh7 * kp6gdh10 * NADP * P6G * Ru5P + CO2 * kp6gdh1 * kp6gdh3 * (kp6gdh5 + kp6gdh6) * kp6gdh8 * kp6gdh10 * NADP * P6G * Ru5P + kp6gdh3 * kp6gdh5 * kp6gdh7 * kp6gdh10 * kp6gdh12 * NADPH * P6G * Ru5P + CO2 * kp6gdh3 * (kp6gdh5 + kp6gdh6) * kp6gdh8 * kp6gdh10 * kp6gdh12 * NADPH * P6G * Ru5P)
vpfk vpfk Fru6P + MgATP = Fru16P2 + MgADP

VPFK * (-(Fru16P2 * kcatfpfk * MgADP / (Kmpfkfru16p2 * Kmpfkmgadp)) + Fru6P * kcatfpfk * MgATP / (Kmpfkfru6p * Kmpfkmgatp)) / ((1 + Fru16P2 / Kmpfkfru16p2 + Fru6P / Kmpfkfru6p + MgADP / Kmpfkmgadp + Fru16P2 * MgADP / (Kmpfkfru16p2 * Kmpfkmgadp) + MgATP / Kmpfkmgatp + Fru6P * MgATP / (Kmpfkfru6p * Kmpfkmgatp)) * (1 + pow(1 / (pow(10, pH1) * Kapfk), npfk) * pow(1 + ATP / KTpfkatp, 4) * pow(1 + B23PG / KTpfkb23pg, 4) * pow(1 + Mg / KTpfkmg, 4) / (pow(1 + Fru16P2 / Kmpfkfru16p2 + Fru6P / Kmpfkfru6p, 4) * pow(1 + AMP / KRpfkamp, 4) * pow(1 + Glc16P2 / KRpfkglc16p2, 4) * pow(1 + Phos / KRpfkphos, 4))))
vpgk vpgk B13PG + MgADP = P3GA + MgATP

VPGK * (B13PG * kcatfpgk * MgADP / (Kipgkmgadp * Kmpgkb13pg) - kcatrpgk * MgATP * P3GA / (Kipgkmgatp * Kmpgkp3ga)) / (1 + B13PG / Kipgkb13pg + MgADP / Kipgkmgadp + B13PG * MgADP / (Kipgkmgadp * Kmpgkb13pg) + MgATP / Kipgkmgatp + P3GA / Kipgkp3ga + MgATP * P3GA / (Kipgkmgatp * Kmpgkp3ga))
vpglhydrolysis vpglhydrolysis P6GL = P6G

kspontaneouspglhydrolysis * P6GL + VLactonase * klactonase3 * P6GL / ((klactonase2 + klactonase3) / klactonase1 + P6GL)
vpgm vpgm P3GA = P2GA

VPGM * (-(kcatrpgm * P2GA / Kmpgmp2ga) + kcatfpgm * P3GA / Kmpgmp3ga) / (1 + P2GA / Kmpgmp2ga + P3GA / Kmpgmp3ga)
vphostransport vphostransport Phos = Phose

2.85714 * (-kphostransporti * Phose * Ve + kphostransporti * (pow(10, -6.75 + pH1) / pow(rtv, 2) + 1 / rtv) * Ve * Phos / (1 + pow(10, -6.75 + pH1)))
vpk vpk PEP + MgADP = Pyr + MgATP

VPK * (kcatfpk * MgADP * PEP / (KRpkmgadp * KRpkpep) - kcatrpk * MgATP * Pyr / (KRpkmgatp * KRpkpyr)) / ((1 + MgADP / KRpkmgadp + MgATP / KRpkmgatp + PEP / KRpkpep + MgADP * PEP / (KRpkmgadp * KRpkpep) + Pyr / KRpkpyr + MgATP * Pyr / (KRpkmgatp * KRpkpyr)) * (1 + 1.58489319246111 * pow(10, -7) * pow(10, pH1) * pow(1 + ATP / KTpkatp, 4) / (pow(1 + Fru16P2 / KRf16p2 + Glc16P2 / KRg16p2, 4) * pow(1 + PEP / KRpkpep + Pyr / KRpkpyr, 4))))
vpyrtransport vpyrtransport Pyr = Pyre

2.85714 * (-kpyrtransporti * Pyre * Ve + kpyrtransporti * Ve * Pyr / rtv)
vr5pi vr5pi Ru5P = Rib5P

VR5PI * (-(kr5pi2 * kr5pi4 * Rib5P / (kr5pi2 + kr5pi3)) + kr5pi1 * kr5pi3 * Ru5P / (kr5pi2 + kr5pi3)) / (1 + kr5pi1 * Ru5P / (kr5pi2 + kr5pi3) + kr5pi4 * Xu5P / (kr5pi2 + kr5pi3))
vru5pe vru5pe Ru5P = Xu5P

VRu5PE * (kru5pe1 * kru5pe3 * Ru5P / (kru5pe2 + kru5pe3) - kru5pe2 * kru5pe4 * Xu5P / (kru5pe2 + kru5pe3)) / (1 + kru5pe1 * Ru5P / (kru5pe2 + kru5pe3) + kru5pe4 * Xu5P / (kru5pe2 + kru5pe3))
vta vta Sed7P + GraP = Ery4P + Fru6P

VTA * (-Ery4P * Fru6P * kta2 * kta4 * kta6 * kta8 + GraP * kta1 * kta3 * kta5 * kta7 * Sed7P) / (GraP * (kta2 + kta3) * kta5 * kta7 + Ery4P * kta2 * kta4 * (kta6 + kta7) + Fru6P * GraP * (kta2 + kta3) * kta5 * kta8 + Fru6P * (kta2 + kta3) * kta6 * kta8 + Ery4P * Fru6P * kta4 * (kta2 + kta6) * kta8 + GraP * kta1 * kta5 * (kta3 + kta7) * Sed7P + kta1 * kta3 * (kta6 + kta7) * Sed7P + Ery4P * kta1 * kta4 * (kta6 + kta7) * Sed7P)
vtk1 vtk1 TK + Xu5P = TKXu5P

ktk1 * TK * Xu5P - ktk2 * TKXu5P
vtk2 vtk2 TKXu5P = TKG + GraP

ktk3 * TKXu5P - ktk4 * TKG * GraP
vtk3 vtk3 TKG + Rib5P = TKGRib5P

ktk5 * TKG * Rib5P - ktk6 * TKGRib5P
vtk4 vtk4 TKGRib5P = TK + Sed7P

ktk7 * TKGRib5P - ktk8 * TK * Sed7P
vtk5 vtk5 TKG + Ery4P = TKGEry4P

ktk9 * TKG * Ery4P - ktk10 * TKGEry4P
vtk6 vtk6 TKGEry4P = TK + Fru6P

ktk11 * TKGEry4P - ktk12 * TK * Fru6P
vtpi vtpi GraP = GrnP

VTPI * (GraP * kcatftpi / Kmtpigrap - GrnP * kcatrtpi / Kmtpigrnp) / (1 + GraP / Kmtpigrap + GrnP / Kmtpigrnp)

Global parameters

Id Value
Hct 0.5
KRf16p2 0.000005
KRg16p2 0.0001
KRpfkamp 0.0003
KRpfkglc16p2 0.01
KRpfkphos 0.03
KRpkmgadp 0.000474
KRpkmgatp 0.003
KRpkpep 0.000225
KRpkpyr 0.002
KTpfkatp 0.0001
KTpfkb23pg 0.005
KTpfkmg 0.004
KTpkatp 0.00339
Kahb 0.000000251188643150958
Kapfk 0.0000000891250938133746
Kdihkbpg 0.004
Kdihkglc16p2 0.00003
Kdihkglc6p 0.00001
Kdihkgsh 0.003
Kh2bpg 4270000.0
Kh2f 1120000.0
Khadp 5420000.0
Khamp 3090000.0
Khatp 9070000.0
Khbpg 162000000.0
Khf 7560000.0
Khphos 5680000.0
Kialdb23pg 0.0015
Kialdfru16p2 0.0000198
Kialdgrnp 0.000011
Kidgapdhb13pg 0.000001
Kidgapdhgrap 0.000031
Kidldhpyr 0.000101
Kienomg 0.000046
Kienop2ga 0.00014
Kienopep 0.0001105
Kigapdhnad 0.000045
Kigapdhphos 0.00316
Kihkglc 0.000047
Kihkglc6p 0.000047
Kihkmgadp 0.001
Kihkmgatp 0.001
Kildhnad 0.000503
Kildhnadh 0.00000245
Kipgkb13pg 0.0000016
Kipgkmgadp 0.00008
Kipgkmgatp 0.000186
Kipgkp3ga 0.000205
Kkadp 4.8
Kkamp 1.8
Kkatp 14.0
Kkbpg 85.1
Kkf 10.7
Kkhbpg 8.9
Kkhf 3.3
Kkphos 3.0
Kmaldfru16p2 0.0000071
Kmaldgrap 0.000189
Kmaldgrnp 0.000035
Kmenomg 0.000046
Kmenop2ga 0.00014
Kmenopep 0.0001105
Kmgadp 3290.0
Kmgapdhb13pg 0.000000671
Kmgapdhgrap 0.000095
Kmgapdhnad 0.000045
Kmgapdhphos 0.00316
Kmgatp 43200.0
Kmgbpg 7410.0
Kmgfru16p2 363.0
Kmghadp 107.0
Kmghatp 748.0
Kmghbpg 513.0
Kmghf 89.0
Kmgpifru6p 0.000071
Kmgpiglc6p 0.000181
Kmhkmgadp 0.001
Kmhkmgatp 0.001
Kmldhnad 0.000107
Kmldhnadh 0.00000844
Kmldhplac 0.000414
Kmldhppyr 0.000414
Kmpfkfru16p2 0.0005
Kmpfkfru6p 0.000075
Kmpfkmgadp 0.00054
Kmpfkmgatp 0.000068
Kmpgkb13pg 0.000002
Kmpgkmgadp 0.0001
Kmpgkmgatp 0.001
Kmpgkp3ga 0.0011
Kmpgmp2ga 0.0000256
Kmpgmp3ga 0.000168
Kmtpigrap 0.000446
Kmtpigrnp 0.0001624
VALD 0.00000037
VENO 0.00000022
VG6PDH 0.000000093
VGDH 0.00000766
VGPI 0.000000218
VGSSGR 0.000000125
VHK 0.000000025
VLDH 0.00000343
VLactonase 0.000014
VP6GDH 0.0000021
VPFK 0.00000011
VPGK 0.00000274
VPGM 0.00000041
VPK 0.000000087
VR5PI 0.0000142
VRu5PE 0.00000422
VTA 0.00000069
VTPI 0.00000114
Ve 0.5
Vi 0.35
alpha 0.7
k1 0.15
katpase 0.000585
kbpgsp10 1979.0
kbpgsp11 0.01
kbpgsp12 1000.0
kbpgsp14 1000000000.0
kbpgsp15 610000.0
kbpgsp16 0.19
kbpgsp2 400.0
kbpgsp5 100000000.0
kbpgsp7 1000.0
kbpgsp8 10000.0
kbpgsp9 0.55
kcatfald 68.0
kcatfeno 190.0
kcatfgpi 1470.0
kcatfldh 458.0
kcatfpfk 822.0
kcatfpgk 2290.0
kcatfpgm 795.0
kcatfpk 1386.0
kcatftpi 14560.0
kcatrald 234.0
kcatreno 50.0
kcatrgpi 1760.0
kcatrldh 115.0
kcatrpfk 36.0
kcatrpgk 917.0
kcatrpgm 714.0
kcatrpk 3.26
kcatrtpi 1280.0
kfldhp 0.00346
kg6pdh1 110000000.0
kg6pdh10 1400000000.0
kg6pdh2 870.0
kg6pdh3 26000000.0
kg6pdh4 300.0
kg6pdh5 750.0
kg6pdh6 2000.0
kg6pdh7 220000.0
kg6pdh8 1100000000.0
kg6pdh9 10000.0
kgssgr1 85000000.0
kgssgr10 50000000.0
kgssgr11 7000.0
kgssgr12 100000000.0
kgssgr2 510.0
kgssgr3 1000000000.0
kgssgr4 72000.0
kgssgr5 810.0
kgssgr6 1000.0
kgssgr7 1000000.0
kgssgr8 50000000.0
kgssgr9 1000000.0
khbadpd 1200.0
khbatpd 1200.0
khbb13pgd 1200.0
khbbpgd 1200.0
khbmgatpd 1200.0
klactonase1 13000000.0
klactonase2 1000.0
klactonase3 29.0
klactransporti 0.0036
kmgadpd 1200.0
kmgatpd 1200.0
kmgb13pgd 1200.0
kmgbpgd 1200.0
kmgf16p2d 1200.0
kmgphosd 1200.0
kox 0.000034
koxNADH 0.0163
kp6gdh1 2400000.0
kp6gdh10 225000.0
kp6gdh11 300.0
kp6gdh12 4950000.0
kp6gdh2 410.0
kp6gdh3 2000000000.0
kp6gdh4 26000.0
kp6gdh5 48.0
kp6gdh6 30.0
kp6gdh7 630.0
kp6gdh8 36000.0
kp6gdh9 800.0
kphostransporti 0.00056
kpyrtransporti 0.018
kr5pi1 60900.0
kr5pi2 33.3
kr5pi3 14.2
kr5pi4 21600.0
krldhp 0.000000543
kru5pe1 3910000.0
kru5pe2 438.0
kru5pe3 305.0
kru5pe4 1490000.0
kspontaneouspglhydrolysis 0.00071
kta1 580000.0
kta2 45.3
kta3 16.3
kta4 1010000.0
kta5 490000.0
kta6 60.0
kta7 17.0
kta8 79000.0
ktk1 216000.0
ktk10 175.0
ktk11 40.0
ktk12 21300.0
ktk2 38.0
ktk3 34.0
ktk4 156000.0
ktk5 329000.0
ktk6 175.0
ktk7 40.0
ktk8 44800.0
ktk9 2240000.0
npfk 5.0
pH1 7.2
rtv 0.69

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments