Model Mathematics

\frac{d}{d time} (Glc_i) = V_glucose_transport - V_HK

Glc_6_P = \frac{hexose_P}{Keq_PGI} Keq_PGI = \frac{Fru_6_P}{Glc_6_P}

Fru_6_P = \frac{hexose_P}{Glc_6_P}

\frac{d}{d time} (hexose_P) = V_HK - V_PFK

\frac{d}{d time} (Fru_1_6_BP) = V_PFK - V_ALD

GA_3_P = Keq_TIM DHAP

\frac{d}{d time} (triose_P) = 2.0 V_ALD + V_GPO - (V_GAPDH + V_GDH)

\frac{d}{d time} (one_three_BPGA) = V_GAPDH - V_PGK

three_PGA = \frac{N}{1.0 + Keq_PGM + Keq_PGM Keq_ENO}

two_PGA = Keq_PGM three_PGA

\frac{d}{d time} (N) = V_PGK - V_PYK

PEP = Keq_ENO two_PGA

\frac{d}{d time} (pyruvate_i) = V_PYK - V_pyruvate_transport

DHAP = \frac{triose_P}{1.0 + Keq_TIM}

\frac{d}{d time} (Gly_3_P) = V_GDH - (V_GK + V_GPO)

NAD = C7 - NADH

\frac{d}{d time} (NADH) = V_GAPDH - V_GDH

\frac{d}{d time} (P) = V_PGK + V_GK + V_PYK - (V_HK + V_PFK + V_ATP_utilisation)

ATP = \frac{(C6 - (- (P (1.0 - (4.0 Keq_AK))))) + {({(C6 - (- (P (1.0 - (4.0 Keq_AK)))))}^{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))}

ADP = P - (2.0 ATP)

AMP = C6 - (ATP + ADP)

C6 = ATP + ADP + AMP

C7 = NADH + NAD

V_glucose_transport = V_glucose_transport_max \frac{Glc_o - Glc_i}{K_Glc + Glc_o + Glc_i + alpha Glc_o \frac{Glc_i}{K_Glc}}

V_pyruvate_transport = V_pyruvate_transport_max \frac{pyruvate_i}{K_pyruvate} (1.0 + \frac{pyruvate_i}{K_pyruvate})

V_GPO = V_GPO_max \frac{Gly_3_P}{K_Gly_3_P} (1.0 + \frac{Gly_3_P}{K_Gly_3_P})

V_HK = V_HK_max \frac{\frac{Glc_i}{K_Glc_i}}{1.0 + \frac{Glc_i}{K_Glc_i} + \frac{Glc_6_P}{K_Glc_6_P}} \frac{\frac{ATP}{K_ATP}}{1.0 + \frac{ATP}{K_ATP} + \frac{ADP}{K_ADP}}

V_GAPDH = V_GAPDH_max_plus \frac{\frac{GA_3_P}{K_GA_3_P} (\frac{NAD}{K_NAD} - V_GAPDH_max_ratio) \frac{one_three_BPGA}{K_one_three_BPGA} \frac{NADH}{K_NADH}}{(1.0 + \frac{GA_3_P}{K_GA_3_P} + \frac{one_three_BPGA}{K_one_three_BPGA}) (1.0 + \frac{NAD}{K_NAD} + \frac{NADH}{K_NADH})}

V_PGK = V_PGK_max_plus \frac{\frac{one_three_BPGA}{K_one_three_BPGA} (\frac{ADP}{K_ADP} - V_PGK_max_ratio) \frac{three_PGA}{K_3_PGA} \frac{ATP}{K_ATP}}{(1.0 + \frac{one_three_BPGA}{K_one_three_BPGA} + \frac{three_PGA}{K_3_PGA}) (1.0 + \frac{ADP}{K_ADP} + \frac{ATP}{K_ATP})}

V_GK = V_GK_max_plus \frac{\frac{Gly_3_P}{K_Gly_3_P} (\frac{ADP}{K_ADP} - V_GK_max_ratio) \frac{glycerol}{K_glycerol} \frac{ATP}{K_ATP}}{(1.0 + \frac{Gly_3_P}{K_Gly_3_P} + \frac{glycerol}{K_glycerol}) (1.0 + \frac{ADP}{K_ADP} + \frac{ATP}{K_ATP})}

V_GDH = V_GDH_max_plus \frac{\frac{DHAP}{K_DHAP} (\frac{NADH}{K_NADH} - V_GDH_max_ratio) \frac{Gly_3_P}{K_Gly_3_P} \frac{NAD}{K_NAD}}{(1.0 + \frac{DHAP}{K_DHAP} + \frac{Gly_3_P}{K_Gly_3_P}) (1.0 + \frac{NADH}{K_NADH} + \frac{NAD}{K_NAD})}

V_PFK = V_PFK_max \frac{Ki_1}{Fru_1_6_BP + Ki_1} \frac{\frac{Fru_6_P}{KM_Fru_6_P}}{1.0 + \frac{Fru_6_P}{KM_Fru_6_P} + \frac{Fru_1_6_BP}{Ki_2}} \frac{\frac{ATP}{KM_ATP}}{1.0 + \frac{ATP}{KM_ATP}}

V_PYK = V_PYK_max \frac{{(\frac{PEP}{KM_PEP})}^{n}}{1.0 + {(\frac{PEP}{KM_PEP})}^{n}} \frac{\frac{ADP}{KM_ADP}}{1.0 + \frac{ADP}{KM_ADP}} KM_PEP = 0.34 (1.0 + \frac{ATP}{0.57} + \frac{ADP}{0.64})

V_ALD = V_ALD_max_plus \frac{\frac{Fru_1_6_BP}{KM_Fru_1_6_BP} - (V_ALD_max_ratio \frac{GA_3_P}{DHAP} KM_GA_3_P KM_DHAP)}{1.0 + \frac{Fru_1_6_BP}{KM_Fru_1_6_BP} + \frac{GA_3_P}{KM_GA_3_P} + \frac{DHAP}{KM_DHAP} + \frac{Fru_1_6_BP GA_3_P}{KM_Fru_1_6_BP Ki_GA_3_P} + \frac{DHAP GA_3_P}{KM_DHAP KM_GA_3_P}} KM_Fru_1_6_BP = 9.0 e -3 (1.0 + \frac{ATP}{0.68} + \frac{ADP}{1.51} + \frac{AMP}{3.65})

V_ATP_utilisation = k \frac{ATP}{ADP}