You are here: Home / Exposures / Bakker, Mensonides, Teusink, van Hoek, Michels, Westerhoff, 2000 / Compartmentation protects trypanosomes from the dangerous design of glycolysis

Model Mathematics

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Component: environment

Component: GlcI

\frac{d}{d time} (GlcI) = vGlcTr - vHK

Component: hexose_P

\frac{d}{d time} (hexose_P) = vHK - vPFK

Component: Fru16BP

\frac{d}{d time} (Fru16BP) = vPFK - vALD

Component: triose_P

\frac{d}{d time} (triose_P) = 2.0 vALD + vGPO - (vGAPDH + vGDH)

Component: BPGA13

\frac{d}{d time} (BPGA13) = vGAPDH - vPGK

Component: N

\frac{d}{d time} (N) = vPGK - vPK

Component: Pyr

\frac{d}{d time} (Pyr) = vPK - vPyrTr

Component: NADH

\frac{d}{d time} (NADH) = vGAPDH - vGDH

Component: NAD

\frac{d}{d time} (NAD) = vGDH - vGAPDH

Component: Gly3P

\frac{d}{d time} (Gly3P) = vGDH - (vGlyK + vGPO)

Component: Gly

\frac{d}{d time} (Gly) = vGlyK

Component: P

\frac{d}{d time} (P) = vPGK + vGlyK + vPK - (vHK + vPFK + vATPase)

Component: ATP

ATP = \frac{(P (1.0 - (4.0 Keq_AK)) - sumA) + {({(sumA - ((1.0 - (4.0 Keq_AK)) P))}^{2.0} + 4.0 (1.0 - (4.0 Keq_AK)) (- Keq_AK) P^{2.0})}^{0.5}}{2.0 (1.0 - (4.0 Keq_AK))}

Component: ADP

ADP = P - (2.0 ATP)

Component: DHAP

DHAP = \frac{sumc5 DHAP}{sumc4 + sumc5 - (BPGA13 + 2 Fru16BP + Fru6P + GAP + Glc6P + P)}

Component: GAP

GAP = triose_P - DHAP

Component: GlcE

GlcE = \{\begin{matrix} 5.0 if time \geq 60.0 \land time < 61.0 \\ 0.05 otherwise \end{matrix}

Component: Glc6P

\frac{d}{d time} (Glc6P) = vHK - vPGI

Component: Fru6P

Fru6P = hexose_P - Glc6P

Component: PGA3

PGA3 = N - PEP

Component: PEP

PEP = Keq_ENO Keq_PGM PGA3

Component: vGlcTr

vGlcTr = vGlcTr_max \frac{GlcE - GlcI}{K_Glc + GlcE + GlcI + alpha GlcE \frac{GlcI}{K_Glc}}

Component: vHK

vHK = \frac{vHK_max GlcI ATP}{K_ATP K_GlcI (1.0 + \frac{Glc6P}{K_Glc6P} + \frac{GlcI}{K_GlcI}) (1.0 + \frac{ATP}{K_ATP} + \frac{ADP}{K_ADP})}

Component: vPGI

vPGI = \frac{vPGI_max (\frac{Glc6P}{K_Glc6P} - (\frac{Fru6P}{K_Fru6P}))}{1 + \frac{Glc6P}{K_Glc6P} + \frac{Fru6P}{K_Fru6P}}

Component: vPFK

vPFK = \frac{Ki_1 vPFK_max Fru6P ATP}{KM_ATP KM_Fru6P (Fru16BP + Ki_1) (1.0 + \frac{Fru16BP}{Ki_2} + \frac{Fru6P}{KM_Fru6P}) (1.0 + \frac{ATP}{KM_ATP})}

Component: vALD

vALD = \frac{\frac{vALD_max_forward Fru16BP}{0.009 (1 + \frac{ATP}{0.68} + \frac{ADP}{1.51} + \frac{sumA - (ATP + ADP)}{3.65})} - (\frac{vALD_max_reverse GAP DHAP}{KM_DHAP KM_GAP})}{1 + \frac{GAP}{KM_GAP} + \frac{DHAP}{KM_DHAP} + \frac{GAP DHAP}{KM_DHAP KM_GAP} + \frac{Fru16BP}{0.009 (1 + \frac{ATP}{0.68} + \frac{ADP}{1.51} + \frac{sumA - (ATP + ADP)}{3.65})} + \frac{Fru16BP GAP}{Ki_GAP 0.009 (1 + \frac{ATP}{0.68} + \frac{ADP}{1.51} + \frac{sumA - (ATP + ADP)}{3.65})}}

Component: vTPI

vTPI = \frac{vTPI_max (\frac{DHAP}{K_DHAP} - (\frac{5.7 GAP}{K_GAP}))}{1.0 + \frac{GAP}{K_GAP} + \frac{DHAP}{K_DHAP}}

Component: vGAPDH

vGAPDH = vGAPDH_max \frac{vGAPDH_max_forward (GAP \frac{\frac{NAD}{K_GAP}}{K_NAD} - (\frac{vGAPDH_max_reverse}{vGAPDH_max_forward} \frac{\frac{BPGA13 NADH}{K_BPGA13}}{K_NADH}))}{(1 + \frac{GAP}{K_GAP} + \frac{BPGA13}{K_BPGA13}) (1 + \frac{NAD}{K_NAD} + \frac{NADH}{K_NADH})}

Component: vGDH

vGDH = \frac{vGDH_max vGDH_max_forward (\frac{NADH DHAP}{K_NADH K_DHAP} - (\frac{vGDH_max_reverse NAD Gly3P}{K_Gly3P K_NAD vGDH_max_forward}))}{(1 + \frac{NAD}{K_NAD} + \frac{NADH}{K_NADH}) (1 + \frac{DHAP}{K_DHAP} + \frac{Gly3P}{K_Gly3P})}

Component: vGPO

vGPO = \frac{vGPO_max Gly3P}{Gly3P + K_Gly3P}

Component: vPyrTr

vPyrTr = \frac{\frac{vPyrTr_max Pyr}{K_pyruvate}}{1.0 + \frac{Pyr}{K_pyruvate}}

Component: vPGK

vPGK = \frac{vPGK_max vPGK_max_forward (\frac{(- vPGK_max_reverse) PGA3 ATP}{K_ATP K_PGA3 vPGK_max_forward} + \frac{BPGA13 ADP}{K_BPGA13 K_ADP})}{(1 + \frac{BPGA13}{K_BPGA13} + \frac{PGA3}{K_PGA3}) (1 + \frac{ADP}{K_ADP} + \frac{ATP}{K_ATP})}

Component: vPK

vPK = \frac{\frac{vPK_max {(\frac{PEP}{0.34 (1 + \frac{ATP}{0.57} + \frac{ADP}{0.64})})}^{n} ADP}{KM_ADP}}{(1 + {(\frac{PEP}{0.34 (1 + \frac{ATP}{0.57} + \frac{ADP}{0.64})})}^{n}) (1 + \frac{ADP}{KM_ADP})}

Component: vATPase

vATPase = \frac{k ATP}{ADP}

Component: vGlyK

vGlyK = \frac{vGlyK_max (\frac{vGlyK_max_forward ADP Gly3P}{K_ADP K_Gly3P} - (\frac{vGlyK_max_reverse ATP Gly}{K_ATP K_Gly}))}{(1 + \frac{Gly3P}{K_Gly3P} + \frac{Gly}{K_Gly}) (1 + \frac{ADP}{K_ADP} + \frac{ATP}{K_ATP})}

Source: Derived from workspace Bakker, Mensonides, Teusink, Vanhoek, Michels, Westerhoff, 2000 at changeset f19dbed3b2aa.

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Compartmentation protects trypanosomes from the dangerous design of glycolysis