JWS Online

Model

Name

penkler2

Notes

Substance units

fmol/trophozoite

Time units

min

Volume units

Area units

None

Length units

None

Reaction extent units

fmol/trophozoite

Construction and validation of a detailed kinetic model of glycolysis in Plasmodium falciparum.

Gerald Penkler
Francois du Toit
Waldo Adams
Marina Rautenbach
Daniel C Palm
David D van Niekerk
Jacky L Snoep

FEBS J. 2015; 282 (8): 1481-1511

PubMed: 25693925
DOI: 10.1111/febs.13237
ISSN: 1742-4658
URL: http://ncbi.nlm.nih.gov/pubmed/25693925

Abstract

UNLABELLED: The enzymes in the Embden-Meyerhof-Parnas pathway of Plasmodium falciparum trophozoites were kinetically characterized and their integrated activities analyzed in a mathematical model. For validation of the model, we compared model predictions for steady-state fluxes and metabolite concentrations of the hexose phosphates with experimental values for intact parasites. The model, which is completely based on kinetic parameters that were measured for the individual enzymes, gives an accurate prediction of the steady-state fluxes and intermediate concentrations. This is the first detailed kinetic model for glucose metabolism in P. falciparum, one of the most prolific malaria-causing protozoa, and the high predictive power of the model makes it a strong tool for future drug target identification studies. The modelling workflow is transparent and reproducible, and completely documented in the SEEK platform, where all experimental data and model files are available for download.
DATABASE: The mathematical models described in the present study have been submitted to the JWS Online Cellular Systems Modelling Database (http://jjj.bio.vu.nl/database/penkler). The investigation and complete experimental data set is available on SEEK (10.15490/seek.1.
INVESTIGATION: 56).

Unit definitions 12

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
—	0.016666666666666666 second^(-1.0)
—	1.0 mole
—	1.0 litre
—	60.0 second
—	1.0 mole litre^(-1.0)
—	1e-15 litre
—	0.016666666666666666 litre^(-1.0) mole second^(-1.0)
—	1e-15 mole
—	1000.0 gram litre^(-1.0)
—	1e-15 mole
—	1.6666666666666667e-05 second^(-1.0) gram^(-1.0) mole
—	1.0 dimensionless

Compartments 2

Id	Name	Spatial dimensions	Size
Vex	Vex	3.0	2637.68 fL
Vpf	Vpf	3.0	28.0 fL

Species 21

Id	Name	Initial quantity	Compartment	Fixed
adpPF	adpPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
atpPF	atpPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
b13pgPF	b13pgPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
dhapPF	dhapPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
f16bpPF	f16bpPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
f6pPF	f6pPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
g3pPF	g3pPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
g6pPF	g6pPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
gapPF	gapPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
glcEX	glcEX	<initial assignment> fmol/external volume	Vex (Vex)	✘
glcPF	glcPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
glyEX	glyEX	<initial assignment> fmol/external volume	Vex (Vex)	✘
lacEX	lacEX	<initial assignment> fmol/external volume	Vex (Vex)	✘
lacPF	lacPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
nadPF	nadPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
nadhPF	nadhPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
p2gPF	p2gPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
p3gPF	p3gPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
pepPF	pepPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘
pyrEX	pyrEX	<initial assignment> fmol/external volume	Vex (Vex)	✘
pyrPF	pyrPF	<initial assignment> fmol/trophozoite	Vpf (Vpf)	✘

Initial assignments 21

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
adpPF = ConcAdpPF * Vpf
glcEX = ConcGlcEX * Vex
pepPF = ConcPepPF * Vpf
nadhPF = ConcNadhPF * Vpf
atpPF = ConcAtpPF * Vpf
g3pPF = ConcGly3pPF * Vpf
pyrEX = ConcPyrEX * Vex
nadPF = ConcNadPF * Vpf
glyEX = ConcGlyEX * Vex
glcPF = ConcGlcPF * Vpf
pyrPF = ConcPyrPF * Vpf
lacPF = ConcLacPF * Vpf
f6pPF = ConcF6pPF * Vpf
dhapPF = ConcDhapPF * Vpf
b13pgPF = ConcB13pgPF * Vpf
g6pPF = ConcG6pPF * Vpf
lacEX = ConcLacEX * Vex
gapPF = ConcGapPF * Vpf
p2gPF = ConcP2gPF * Vpf
p3gPF = ConcP3gPF * Vpf
f16bpPF = ConcF16bpPF * Vpf

Reactions 17

Id	Name	Reaction Equation and Kinetic Law
vPFvALD	vPFvALD	f16bpPF = dhapPF + gapPF Vpf * VPFvALD * f16bpPF / (Kf16bpPFvALD * Vpf) * (1 - dhapPF * gapPF / f16bpPF / (Vpf * KeqPFvALD)) / (1 + dhapPF / (KdhapPFvALD * Vpf) + gapPF / (KgapPFvALD * Vpf) + f16bpPF / (Kf16bpPFvALD * Vpf) + dhapPF * gapPF / (KgapPFvALD * KdhapPFvALD * Vpf * Vpf))
vPFvATPASE	vPFvATPASE	atpPF = adpPF Vpf * VPFvATPASE * pow(atpPF / (KmPFvATPASE * Vpf), 5) / (1 + pow(atpPF / (KmPFvATPASE * Vpf), 5))
vPFvENO	vPFvENO	p2gPF = pepPF Vpf * VPFvENO * p2gPF / (Kp2gPFvENO * Vpf) * (1 - pepPF / (p2gPF * KeqPFvENO)) / (1 + p2gPF / (Kp2gPFvENO * Vpf) + pepPF / (KpepPFvENO * Vpf))
vPFvG3PDH	vPFvG3PDH	nadhPF + dhapPF = g3pPF + nadPF Vpf * VfPFvG3PDH * dhapPF * nadhPF / (KdhapPFvG3PDH * KnadhPFvG3PDH * Vpf * Vpf) * (1 - g3pPF / Vpf * nadPF / Vpf / (KeqPFvG3PDH * dhapPF / Vpf * nadhPF / Vpf)) / ((1 + nadPF / (KnadPFvG3PDH * Vpf) + nadhPF / (KnadhPFvG3PDH * Vpf)) * (1 + g3pPF / (Kg3pPFvG3PDH * Vpf) + dhapPF / (KdhapPFvG3PDH * Vpf)))
vPFvGAPDH	vPFvGAPDH	gapPF + nadPF = nadhPF + b13pgPF (Vpf * VPFvGAPDH * gapPF * nadPF / (KgapPFvGAPDH * KnadPFvGAPDH * Vpf * Vpf) - Vpf * VrPFvGAPDH * nadhPF * b13pgPF / (KnadhPFvGAPDH * Kb13pgPFvGAPDH * Vpf * Vpf)) / ((1 + nadPF / (KnadPFvGAPDH * Vpf) + nadhPF / (KnadhPFvGAPDH * Vpf)) * (1 + gapPF / (KgapPFvGAPDH * Vpf) + b13pgPF / (Kb13pgPFvGAPDH * Vpf)))
vPFvGLCtr	vPFvGLCtr	glcEX = glcPF Vpf * VPFvGLCtr / KmPFvGLCtr * (glcEX / Vex - glcPF / Vpf) / (1 + glcEX / (KmPFvGLCtr * Vex) + glcPF / (KmPFvGLCtr * Vpf) + alphaPFvGLCtr * glcEX / (KmPFvGLCtr * Vex) * glcPF / (KmPFvGLCtr * Vpf))
vPFvGLYtr	vPFvGLYtr	g3pPF = glyEX Vpf * kPFvGLYtr * (g3pPF / Vpf - glyEX / Vex)
vPFvHK	vPFvHK	glcPF + atpPF = g6pPF + adpPF Vpf * VPFvHK * glcPF / (KglcPFvHK * Vpf) * atpPF / (KatpPFvHK * Vpf) * (1 - adpPF * g6pPF / (KeqPFvHK * atpPF * glcPF)) / ((1 + atpPF / (KiatpPFvHK * Vpf)) * (1 + adpPF / (KadpPFvHK * Vpf) + atpPF / (KatpPFvHK * Vpf)) * (1 + g6pPF / (Kg6pPFvHK * Vpf) + glcPF / (KglcPFvHK * Vpf)))
vPFvLACtr	vPFvLACtr	lacPF = lacEX Vpf * VPFvLACtr * lacPF / (KlacPFvLACtr * Vpf) * (1 - hEX * lacEX / Vex / (hPF * lacPF / Vpf)) / (1 + lacPF / (KlacPFvLACtr * Vpf) + lacEX / (KlacPFvLACtr * Vex) + pyrPF / (KipyrPFvLACtr * Vpf) + pyrEX / (KipyrPFvLACtr * Vex)) + Vpf * KdPFvLACtr * (1 - hEX * lacEX / Vex / (hPF * lacPF / Vpf)) * lacPF / Vpf
vPFvLDH	vPFvLDH	nadhPF + pyrPF = lacPF + nadPF (Vpf * VfPFvLDH * nadhPF * pyrPF / (KnadhPFvLDH * KpyrPFvLDH * Vpf * Vpf) - Vpf * VrPFvLDH * lacPF * nadPF / (KlacPFvLDH * KnadPFvLDH * Vpf * Vpf)) / ((1 + nadPF / (KnadPFvLDH * Vpf) + nadhPF / (KnadhPFvLDH * Vpf)) * (1 + lacPF / (KlacPFvLDH * Vpf) + pyrPF / (KpyrPFvLDH * Vpf)))
vPFvPFK	vPFvPFK	atpPF + f6pPF = adpPF + f16bpPF Vpf * VPFvPFK * atpPF * f6pPF / (KatpPFvPFK * Vpf * Kf6pPFvPFK * Vpf) / ((1 + atpPF / (KatpPFvPFK * Vpf)) * (1 + adpPF / (KadpPFvPFK * Vpf) + atpPF / (KatpPFvPFK * Vpf)) * (1 + f16bpPF / (Kf16bpPFvPFK * Vpf) + f6pPF / (Kf6pPFvPFK * Vpf)))
vPFvPGI	vPFvPGI	g6pPF = f6pPF Vpf * VPFvPGI * g6pPF / (Kg6pPFvPGI * Vpf) * (1 - f6pPF / (g6pPF * KeqPFvPGI)) / (1 + f6pPF / (Kf6pPFvPGI * Vpf) + g6pPF / (Kg6pPFvPGI * Vpf))
vPFvPGK	vPFvPGK	adpPF + b13pgPF = atpPF + p3gPF Vpf * KadpPFvPGK * Kb13pgPFvPGK * KeqPFvPGK * VrPFvPGK / (KatpPFvPGK * Kp3gPFvPGK) * (KeqPFvPGK / (atpPF * p3gPF / (adpPF * b13pgPF)) - 1) * atpPF * p3gPF / (KatpPFvPGK * Kp3gPFvPGK * Vpf * Vpf) / ((1 + adpPF / (KadpPFvPGK * Vpf) + atpPF / (KatpPFvPGK * Vpf)) * (1 + b13pgPF / (Kb13pgPFvPGK * Vpf) + p3gPF / (Kp3gPFvPGK * Vpf)))
vPFvPGM	vPFvPGM	p3gPF = p2gPF Vpf * VPFvPGM * p3gPF / (Kp3gPFvPGM * Vpf) * (1 - p2gPF / (p3gPF * KeqPFvPGM)) / (1 + p2gPF / (Kp2gPFvPGM * Vpf) + p3gPF / (Kp3gPFvPGM * Vpf))
vPFvPK	vPFvPK	adpPF + pepPF = atpPF + pyrPF Vpf * VPFvPK * adpPF / (KadpPFvPK * Vpf) * pepPF / (KpepPFvPK * Vpf) / ((1 + adpPF / (Vpf * KadpPFvPK)) * (1 + pepPF / (Vpf * KpepPFvPK)) * (1 + LPFvPK * (1 + pow(adpPF / (KiadpPFvPK * Vpf) + atpPF / (KiatpPFvPK * Vpf), h)) * (1 + pow(pepPF / (KipepPFvPK * Vpf) + pyrPF / (KipyrPFvPK * Vpf), h))))
vPFvPYRtr	vPFvPYRtr	pyrPF = pyrEX Vpf * VPFvPYRtr * pyrPF / (KpyrPFvPYRtr * Vpf) * (1 - hEX * pyrEX / Vex / (hPF * pyrPF / Vpf)) / (1 + pyrEX / (KpyrPFvPYRtr * Vex) + pyrPF / (KpyrPFvPYRtr * Vpf) + lacPF / (KilacPFvPYRtr * Vpf) + lacEX / (KilacPFvPYRtr * Vex)) + Vpf * KdPFvPYRtr * (1 - hEX * pyrEX / Vex / (hPF * pyrPF / Vpf)) * pyrPF / Vpf
vPFvTPI	vPFvTPI	dhapPF = gapPF Vpf * VPFvTPI * dhapPF / (KdhapPFvTPI * Vpf) * (1 - gapPF / (KeqPFvTPI * dhapPF)) / (1 + dhapPF / (KdhapPFvTPI * Vpf) + gapPF / (KgapPFvTPI * Vpf) + pepPF / (KipepPFvTPI * Vpf))

Parameters 0 107

Global parameters

Id	Value
ConcAdpPF	0.0015 M
ConcAtpPF	0.0015 M
ConcB13pgPF	0.0001 M
ConcDhapPF	0.0001 M
ConcF16bpPF	0.0001 M
ConcF6pPF	0.0001 M
ConcG6pPF	0.0001 M
ConcGapPF	0.0001 M
ConcGlcEX	0.005 M
ConcGlcPF	0.0001 M
ConcGly3pPF	0.0001 M
ConcGlyEX	3.79121e-11 M
ConcLacEX	3.79121e-11 M
ConcLacPF	0.0001 M
ConcNadPF	0.0015 M
ConcNadhPF	0.0015 M
ConcP2gPF	0.0001 M
ConcP3gPF	0.0001 M
ConcPepPF	1e-05 M
ConcPyrEX	3.79121e-11 M
ConcPyrPF	0.0001 M
KadpPFvHK	0.000846735 M
KadpPFvPFK	0.00074176 M
KadpPFvPGK	0.00015 M
KadpPFvPK	0.000317 M
KatpPFvHK	0.00069647 M
KatpPFvPFK	0.0007862 M
KatpPFvPGK	0.00077 M
Kb13pgPFvGAPDH	2.359e-05 M
Kb13pgPFvPGK	1.34e-05 M
KdPFvLACtr	0.005 /min
KdPFvPYRtr	0.0007 /min
KdhapPFvALD	0.00011 M
KdhapPFvG3PDH	0.00034 M
KdhapPFvTPI	0.001954 M
KeqPFvALD	9e-05 M
KeqPFvENO	4.6 dimensionless
KeqPFvG3PDH	32600.0 dimensionless
KeqPFvHK	1310.0 dimensionless
KeqPFvPGI	0.33 dimensionless
KeqPFvPGK	3200.0 dimensionless
KeqPFvPGM	0.19 dimensionless
KeqPFvTPI	0.04545 dimensionless
Kf16bpPFvALD	6.84e-05 M
Kf16bpPFvPFK	0.003626 M
Kf6pPFvPFK	0.00109454 M
Kf6pPFvPGI	9.6651e-05 M
Kg3pPFvG3PDH	0.00398 M
Kg6pPFvHK	4.3e-05 M
Kg6pPFvPGI	0.00100774 M
KgapPFvALD	4.6e-05 M
KgapPFvGAPDH	0.000917 M
KgapPFvTPI	0.000337 M
KglcPFvHK	0.000168613 M
KiadpPFvPK	0.002 M
KiatpPFvHK	0.026 M
KiatpPFvPK	0.00182 M
KilacPFvPYRtr	0.000358 M
KipepPFvPK	0.00292 M
KipepPFvTPI	1.59e-05 M
KipyrPFvLACtr	0.00163 M
KipyrPFvPK	0.105 M
KlacPFvLACtr	0.0038 M
KlacPFvLDH	0.003611 M
KmPFvATPASE	0.0045 M
KmPFvGLCtr	0.000213 M
KnadPFvG3PDH	0.00051 M
KnadPFvGAPDH	0.0005662 M
KnadPFvLDH	0.000234 M
KnadhPFvG3PDH	9e-05 M
KnadhPFvGAPDH	2.87e-05 M
KnadhPFvLDH	4.6e-05 M
Kp2gPFvENO	0.000521 M
Kp2gPFvPGM	0.000318 M
Kp3gPFvPGK	0.000267 M
Kp3gPFvPGM	0.00173 M
KpepPFvENO	0.00129 M
KpepPFvPK	0.000406 M
KpyrPFvLDH	0.000133 M
KpyrPFvPYRtr	0.0157 M
LPFvPK	0.255 dimensionless
VPFvALD	0.0569593147718 M/min
VPFvATPASE	0.345 M/min
VPFvENO	0.286295503195 M/min
VPFvGAPDH	0.656263383259 M/min
VPFvGLCtr	0.0469 M/min
VPFvHK	0.083 M/min
VPFvLACtr	0.598 M/min
VPFvPFK	0.41 M/min
VPFvPGI	0.800428265477 M/min
VPFvPGM	0.186937901488 M/min
VPFvPK	0.762 M/min
VPFvPYRtr	0.216 M/min
VPFvTPI	1.50599571726 M/min
VfPFvG3PDH	0.012 M/min
VfPFvLDH	0.542612419668 M/min
VrPFvGAPDH	0.243199143455 M/min
VrPFvLDH	0.290792291203 M/min
VrPFvPGK	0.353533190557 M/min
alphaPFvGLCtr	0.91 dimensionless
h	4.0 dimensionless
hEX	<assignment rule> M
hPF	<assignment rule> M
kPFvGLYtr	2.0 /min
pHConversionFactor	1.0 M
phEX	7.1 dimensionless
phPF	7.2 dimensionless

Local parameters

Id	Value	Reaction

Rules 0 0 2

Assignment rules

Definition
hPF = pHConversionFactor / pow(10.0, phPF)
hEX = pHConversionFactor / pow(10.0, phEX)

Rate rules

Definition

Algebraic rules

Definition

Function definitions 0

Definition

Events 0

Trigger	Assignments