mulquiney1

v_RBCvAK

v_RBCvAK

mgadpRBC + adpRBC = mgatpRBC + ampRBC

v_RBCvALD

v_RBCvALD

f16p2RBC = dhapRBC + gapRBC

v_RBCvATPASE

v_RBCvATPASE

mgatpRBC = mgadpRBC + phosRBC

v_RBCvBPGSP1

v_RBCvBPGSP1

b13pgRBC + bpgspRBC = bpgspb13pgRBC

v_RBCvBPGSP2

v_RBCvBPGSP2

bpgspb13pgRBC = bpgsppRBC + p3gRBC

v_RBCvBPGSP3

v_RBCvBPGSP3

bpgsppRBC + p3gRBC = bpgsppp3gRBC

v_RBCvBPGSP4

v_RBCvBPGSP4

bpgsppRBC + p2gRBC = bpgsppp2gRBC

v_RBCvBPGSP5

v_RBCvBPGSP5

bpgsppp3gRBC = bpgspb23pgRBC

v_RBCvBPGSP6

v_RBCvBPGSP6

bpgsppp2gRBC = bpgspb23pgRBC

v_RBCvBPGSP7

v_RBCvBPGSP7

bpgspb23pgRBC = bpgspRBC + b23pgRBC

v_RBCvBPGSP8

v_RBCvBPGSP8

bpgsppRBC + phosRBC = bpgsppphosRBC

v_RBCvBPGSP9

v_RBCvBPGSP9

bpgsppphosRBC = bpgspRBC + {2.0}phosRBC

v_RBCvENO

v_RBCvENO

p2gRBC = pepRBC

v_RBCvG6PDH

v_RBCvG6PDH

g6pRBC + nadpRBC = nadphRBC + p6glRBC

v_RBCvGAPDH

v_RBCvGAPDH

gapRBC + phosRBC + nadRBC = nadhRBC + b13pgRBC

v_RBCvGSSGR

v_RBCvGSSGR

nadphRBC + gssgRBC = {2.0}gshRBC + nadpRBC

v_RBCvHBADP

v_RBCvHBADP

hbRBC + adpRBC = hbadpRBC

v_RBCvHBATP

v_RBCvHBATP

hbRBC + atpRBC = hbatpRBC

v_RBCvHBB13PG

v_RBCvHBB13PG

hbRBC + b13pgRBC = hbb13pgRBC

v_RBCvHBB23PG

v_RBCvHBB23PG

hbRBC + b23pgRBC = hbb23pgRBC

v_RBCvHBMGATP

v_RBCvHBMGATP

mgatpRBC + hbRBC = hbmgatpRBC

v_RBCvHK

v_RBCvHK

mgatpRBC + glcRBC = g6pRBC + mgadpRBC

v_RBCvLACTRANSPORT

v_RBCvLACTRANSPORT

lacRBC = lacEXT

v_RBCvLDH

v_RBCvLDH

nadhRBC + pyrRBC = lacRBC + nadRBC

v_RBCvLDHP

v_RBCvLDHP

nadphRBC + pyrRBC = lacRBC + nadpRBC

v_RBCvMGADP

v_RBCvMGADP

mgRBC + adpRBC = mgadpRBC

v_RBCvMGATP

v_RBCvMGATP

mgRBC + atpRBC = mgatpRBC

v_RBCvMGB13PG

v_RBCvMGB13PG

mgRBC + b13pgRBC = mgb13pgRBC

v_RBCvMGB23PG

v_RBCvMGB23PG

mgRBC + b23pgRBC = mgb23pgRBC

v_RBCvMGF16P2

v_RBCvMGF16P2

mgRBC + f16p2RBC = mgf16p2RBC

v_RBCvMGG16P2

v_RBCvMGG16P2

mgRBC + g16p2RBC = mgg16p2RBC

v_RBCvMGPHOS

v_RBCvMGPHOS

mgRBC + phosRBC = mgphosRBC

v_RBCvOX

v_RBCvOX

{2.0}gshRBC = gssgRBC

v_RBCvOXNADH

v_RBCvOXNADH

nadhRBC = nadRBC

v_RBCvP6GDH

v_RBCvP6GDH

p6gRBC + nadpRBC = nadphRBC + co2RBC + ru5pRBC

v_RBCvPFK

v_RBCvPFK

mgatpRBC + f6pRBC = f16p2RBC + mgadpRBC

v_RBCvPGI

v_RBCvPGI

g6pRBC = f6pRBC

v_RBCvPGK

v_RBCvPGK

b13pgRBC + mgadpRBC = mgatpRBC + p3gRBC

v_RBCvPGLHYDROLYSIS

v_RBCvPGLHYDROLYSIS

p6glRBC = p6gRBC

v_RBCvPGM

v_RBCvPGM

p3gRBC = p2gRBC

v_RBCvPHOSTRANSPORT

v_RBCvPHOSTRANSPORT

phosRBC = phosEXT

v_RBCvPK

v_RBCvPK

pepRBC + mgadpRBC = pyrRBC + mgatpRBC

v_RBCvPYRTRANSPORT

v_RBCvPYRTRANSPORT

pyrRBC = pyrEXT

v_RBCvR5PI

v_RBCvR5PI

ru5pRBC = rib5pRBC

v_RBCvRu5PE

v_RBCvRu5PE

ru5pRBC = xu5pRBC

v_RBCvTA

v_RBCvTA

sed7pRBC + gapRBC = ery4pRBC + f6pRBC

v_RBCvTIM

v_RBCvTIM

gapRBC = dhapRBC

v_RBCvTK1

v_RBCvTK1

xu5pRBC + tkRBC = tkxu5pRBC

v_RBCvTK2

v_RBCvTK2

tkxu5pRBC = tkgRBC + gapRBC

v_RBCvTK3

v_RBCvTK3

tkgRBC + rib5pRBC = tkgrib5pRBC

v_RBCvTK4

v_RBCvTK4

tkgrib5pRBC = tkRBC + sed7pRBC

v_RBCvTK5

v_RBCvTK5

tkgRBC + ery4pRBC = tkgery4pRBC

v_RBCvTK6

v_RBCvTK6

tkgery4pRBC = tkRBC + f6pRBC

Global parameters

Assignment rules

KaappRBCvHBB13PG = KaRBCvHBB13PG * HbpHRBC

KiappgapRBCvGAPDH = KigapRBCvGAPDH / (1.0 + pow(10.0, -phRBC) / pow(10.0, -7.5) + pow(10.0, -10.0) / pow(10.0, -phRBC))

K13appRBCvBPGSP7 = K13RBCvBPGSP7 * ((1.0 + pow(pow(10.0, -7.2) / pow(10.0, -7.17), 4.0)) / (1.0 + pow(pow(10.0, -phRBC) / pow(10.0, -7.17), 4.0)))

KaappRBCvMGB23PG = KaRBCvMGB23PG * CRBCvMGB23PG * (KRBCvMGB23PG + KhbpgRBCvMGB23PG * KmghbpgRBCvMGB23PG * hRBC) / (1.0 + KhbpgRBCvMGB23PG * hRBC + Kh2bpgRBCvMGB23PG * KhbpgRBCvMGB23PG * hRBC * hRBC + kRBC * KkbpgRBCvMGB23PG + kRBC * KhbpgRBCvMGB23PG * KkhbpgRBCvMGB23PG * hRBC)

KaappRBCvMGF16P2 = KaRBCvMGF16P2 * CRBCvMGF16P2 * (KRBCvMGF16P2 + KhfRBCvMGF16P2 * KmghfRBCvMGF16P2 * hRBC) / (1.0 + KhfRBCvMGF16P2 * hRBC + Kh2fRBCvMGF16P2 * KhfRBCvMGF16P2 * hRBC * hRBC + kRBC * KkfRBCvMGF16P2 + kRBC * KhfRBCvMGF16P2 * KkhfRBCvMGF16P2 * hRBC)

K6appRBCvBPGSP4 = K6RBCvBPGSP4 * ((1.0 + pow(pow(10.0, -7.2) / pow(10.0, -7.17), 4.0)) / (1.0 + pow(pow(10.0, -phRBC) / pow(10.0, -7.17), 4.0)))

K1appRBCvAK = K1RBCvAK * (1.0 + pHConversionFactor * pow(10.0, -phRBC) * KhadpRBCvAK + kRBC * KkadpRBCvAK)

KaappRBCvMGATP = KaRBCvMGATP * CRBCvMGATP * ((KRBCvMGATP + KhatpRBCvMGATP * KmghatpRBCvMGATP * hRBC) / (1.0 + KhatpRBCvMGATP / pHConversionFactor / pow(10.0, phRBC) + kRBC * KkatpRBCvMGATP))

KaappRBCvMGG16P2 = KaRBCvMGG16P2 * CRBCvMGG16P2 * (KRBCvMGG16P2 + KhfRBCvMGG16P2 * KmghfRBCvMGG16P2 * hRBC) / (1.0 + KhfRBCvMGG16P2 * hRBC + Kh2fRBCvMGG16P2 * KhfRBCvMGG16P2 * hRBC * hRBC + kRBC * KkfRBCvMGG16P2 + kRBC * KhfRBCvMGG16P2 * KkhfRBCvMGG16P2 * hRBC)

K2appRBCvAK = K2RBCvAK * (1.0 + hRBC * KhampRBCvAK + kRBC * KkampRBCvAK)

KaappRBCvMGB13PG = KaRBCvMGB13PG * CRBCvMGB13PG * (KRBCvMGB13PG + KhbpgRBCvMGB13PG * KmghbpgRBCvMGB13PG * hRBC) / (1.0 + KhbpgRBCvMGB13PG * hRBC + Kh2bpgRBCvMGB13PG * KhbpgRBCvMGB13PG * hRBC * hRBC + kRBC * KkbpgRBCvMGB13PG + kRBC * KhbpgRBCvMGB13PG * KkhbpgRBCvMGB13PG * hRBC)

KaappRBCvMGPHOS = KaRBCvMGPHOS * (1.0 + pHConversionFactor * pow(10.0, -7.2) * KhphosRBCvMGPHOS + kRBC * KkphosRBCvMGPHOS) / (1.0 + hRBC * KhphosRBCvMGPHOS + kRBC * KkphosRBCvMGPHOS)

KoRBCvPHOSTRANSPORT = KiRBCvPHOSTRANSPORT / KeqRBCvPHOSTRANSPORT

KaappRBCvMGADP = KaRBCvMGADP * CRBCvMGADP * ((KRBCvMGADP + KhadpRBCvMGADP * KmghadpRBCvMGADP * hRBC) / (1.0 + KhadpRBCvMGADP * hRBC + kRBC * KkadpRBCvMGADP))

KiapppyrRBCvLDH = KipyrRBCvLDH * ((1.0 + pow(10.0, -6.8) / pow(10.0, -phRBC)) / (1.0 + pow(10.0, -6.8) / pow(10.0, -7.2)))

KcatrappRBCvGAPDH = KcatrRBCvGAPDH / (1.0 + pow(10.0, -phRBC) / pow(10.0, -7.5) + pow(10.0, -10.0) / pow(10.0, -phRBC))

KmapplacRBCvLDH = KmlacRBCvLDH * ((1.0 + pow(10.0, -phRBC) / pow(10.0, -6.8)) / (1.0 + pow(10.0, -7.2) / pow(10.0, -6.8)))

KeqRBCvLACTRANSPORT = (1.0 + pow(10.0, phRBC - 3.73)) / (1.0 + pow(10.0, phRBC - 3.73) / RtvRBC)

KmappnadhRBCvGAPDH = KmnadhRBCvGAPDH * (pow(10.0, -7.2) / pow(10.0, -phRBC))

KmapppyrRBCvLDH = KmpyrRBCvLDH * ((1.0 + pow(10.0, -6.8) / pow(10.0, -phRBC)) / (1.0 + pow(10.0, -6.8) / pow(10.0, -7.2)))

KcatrappRBCvHK = KcatrRBCvHK / (1.0 + pow(10.0, -phRBC) / pow(10.0, -7.02) + pow(10.0, -9.55) / pow(10.0, -phRBC))

HbpHRBC = (1.0 + 2.0 * KahbRBC / (pHConversionFactor * pow(10.0, -7.2)) + pow(KahbRBC / (pHConversionFactor * pow(10.0, -7.2)), 2.0)) / (1.0 + 2.0 * KahbRBC / hRBC + KahbRBC / hRBC * KahbRBC / hRBC)

KeqRBCvPHOSTRANSPORT = (1.0 + pow(10.0, phRBC - 6.75)) / (1.0 / RtvRBC + pow(10.0, phRBC - 6.75) / (RtvRBC * RtvRBC))

KcatfappRBCvHK = KcatfRBCvHK / (1.0 + pow(10.0, -phRBC) / pow(10.0, -7.02) + pow(10.0, -9.55) / pow(10.0, -phRBC))

KiapplacRBCvLDH = KilacRBCvLDH * ((1.0 + pow(10.0, -phRBC) / pow(10.0, -6.8)) / (1.0 + pow(10.0, -7.2) / pow(10.0, -6.8)))

K4appRBCvBPGSP3 = K4RBCvBPGSP3 * ((1.0 + pow(pow(10.0, -7.2) / pow(10.0, -7.17), 4.0)) / (1.0 + pow(pow(10.0, -phRBC) / pow(10.0, -7.17), 4.0)))

KcatfappRBCvGAPDH = KcatfRBCvGAPDH / (1.0 + pow(10.0, -phRBC) / pow(10.0, -7.5) + pow(10.0, -10.0) / pow(10.0, -phRBC))

atpRBCsum = atpRBC + adpRBC + ampRBC

KoRBCvPYRTRANSPORT = KiRBCvPYRTRANSPORT / RtvRBC

hRBC = pHConversionFactor / pow(10.0, phRBC)

KaappRBCvHBATP = KaRBCvHBATP * HbpHRBC

KaappRBCvHBADP = KaRBCvHBADP * HbpHRBC

KoRBCvLACTRANSPORT = KiRBCvLACTRANSPORT / KeqRBCvLACTRANSPORT

K3appRBCvBPGSP2 = K3RBCvBPGSP2 * ((1.0 + pow(pow(10.0, -7.2) / pow(10.0, -7.17), 4.0)) / (1.0 + pow(pow(10.0, -phRBC) / pow(10.0, -7.17), 4.0)))

KaappRBCvHBBPG = KaRBCvHBBPG * HbpHRBC

KiappnadhRBCvGAPDH = KinadhRBCvGAPDH * (pow(10.0, -7.2) / pow(10.0, -phRBC))

KaappRBCvHBMGATP = KaRBCvHBMGATP * HbpHRBC

K1appRBCvBPGSP1 = K1RBCvBPGSP1 * ((1.0 + pow(10.0, -6.8) / pow(10.0, -7.2)) / (1.0 + pow(10.0, -6.8) / pow(10.0, -phRBC)))

testsum = adpRBC + atpRBC + ampRBC + mgRBC + mgadpRBC + mgatpRBC + mgb13pgRBC + mgb23pgRBC + mgf16p2RBC + mgg16p2RBC + mgphosRBC

Kiappb13pgRBCvGAPDH = Kib13pgRBCvGAPDH / (1.0 + pow(10.0, -phRBC) / pow(10.0, -7.5) + pow(10.0, -10.0) / pow(10.0, -phRBC))

LRBCvPK = pHConversionFactor * pow(10.0, -6.8) / hRBC * pow(1.0 + atpRBC / Vrbc / KtatpRBCvPK, 4.0) / (pow(1.0 + f16p2RBC / Vrbc / Krf16p2RBCvPK + g16p2RBC / Vrbc / Krg16p2RBCvPK, 4.0) * pow(1.0 + pepRBC / Vrbc / KrpepRBCvPK + pyrRBC / Vrbc / KrpyrRBCvPK, 4.0))

lacEXT = ConcLacEXT * vBld

phosEXT = ConcPhosEXT * vBld

pyrEXT = ConcPyrEXT * vBld

glcRBC = ConcGlcRBC * Vrbc

co2RBC = ConcCo2RBC * Vrbc

Function definitions

Note that constraints are not enforced in simulations. It remains the responsibility of the user to verify that simulation results satisfy these constraints.


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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 unexplained. 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 mathematical 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 Mg(2+), 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.

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