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Model Mathematics

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Component: environment

Component: Glc_x_0

Component: Glc_x

\frac{d}{d time} (Glc_x) = inGlc - GlcTrans

Component: Glc

\frac{d}{d time} (Glc) = 59 GlcTrans - HK

Component: G6P

\frac{d}{d time} (G6P) = HK - (PGI + storage)

Component: F6P

\frac{d}{d time} (F6P) = PGI - PFK

Component: FBP

\frac{d}{d time} (FBP) = PFK - ALD

Component: GAP

\frac{d}{d time} (GAP) = ALD + TIM - GAPDH

Component: DHAP

\frac{d}{d time} (DHAP) = ALD - (TIM + lpGlyc)

Component: BPG

\frac{d}{d time} (BPG) = GAPDH - lpPEP

Component: PEP

\frac{d}{d time} (PEP) = lpPEP - PK

Component: Pyr

\frac{d}{d time} (Pyr) = PK - PDC

Component: ATP

\frac{d}{d time} (ATP) = PK + lpPEP - (PFK + storage + HK + consum + AK)

Component: ADP

\frac{d}{d time} (ADP) = PFK + storage + HK + consum + 2 AK - (PK + lpPEP)

Component: AMP

\frac{d}{d time} (AMP) = - AK

Component: CN_x_0

Component: CN_x

\frac{d}{d time} (CN_x) = inCN - lacto

Component: ACA

\frac{d}{d time} (ACA) = PDC - (59 difACA + ADH)

Component: ACA_x

\frac{d}{d time} (ACA_x) = difACA - (lacto + outACA)

Component: EtOH

\frac{d}{d time} (EtOH) = ADH - (59 difEtOH)

Component: EtOH_x

\frac{d}{d time} (EtOH_x) = difEtOH - outEtOH

Component: Glyc

\frac{d}{d time} (Glyc) = lpGlyc - (59 difGlyc)

Component: Glyc_x

\frac{d}{d time} (Glyc_x) = difGlyc - outGlyc

Component: NADH

\frac{d}{d time} (NADH) = GAPDH - (ADH + lpGlyc)

Component: NAD

\frac{d}{d time} (NAD) = ADH + lpGlyc - GAPDH

Component: inGlc

inGlc = k0 (Glc_x_0 - Glc_x)

Component: GlcTrans

GlcTrans = \frac{V_2m}{y_vol} \frac{\frac{Glc_x}{K2_Glc}}{1.0 + \frac{Glc_x}{K2_Glc} + \frac{P2 \frac{Glc_x}{K2_Glc} + 1.0}{P2 \frac{Glc}{K2_Glc} + 1.0} (1.0 + \frac{Glc}{K2_Glc} + \frac{G6P}{K2_IG6P} + \frac{Glc G6P}{K2_Glc K2_IIG6P})} - (\frac{V_2m}{y_vol} \frac{\frac{Glc}{K2_Glc}}{1.0 + \frac{Glc}{K2_Glc} + \frac{P2 \frac{Glc}{K2_Glc} + 1.0}{P2 \frac{Glc_x}{K2_Glc} + 1.0} (1.0 + \frac{Glc_x}{K2_Glc}) + \frac{G6P}{K2_IG6P} + \frac{Glc G6P}{K2_Glc K2_IIG6P}})

Component: HK

HK = \frac{V_3m ATP Glc}{K3_DGlc K3_ATP + K3_Glc ATP + K3_ATP Glc + Glc ATP}

Component: PGI

PGI = \frac{V_4m G6P}{K4_G6P + G6P + \frac{K4_G6P}{K4_F6P} F6P} - (\frac{V_4m \frac{F6P}{K4_eq}}{K4_G6P + G6P + \frac{K4_G6P}{K4_F6P} F6P})

Component: PFK

PFK = \frac{V_5m {F6P}^{2.0}}{K5 (1.0 + kappa5 \frac{ATP}{AMP} \frac{ATP}{AMP}) + {F6P}^{2.0}}

Component: ALD

ALD = \frac{V_6f FBP}{K6_FBP + FBP + \frac{GAP K6_DHAP V_6f}{K6_eq V_6r} + \frac{DHAP K6_GAP V_6f}{K6_eq V_6r} + \frac{FBP GAP}{K6_IGAP} + \frac{GAP DHAP V_6f}{K6_eq V_6r}} - (\frac{V_6f \frac{GAP DHAP}{K6_eq}}{K6_FBP + FBP + \frac{GAP K6_DHAP V_6f}{K6_eq V_6r} + \frac{DHAP K6_GAP V_6f}{K6_eq V_6r} + \frac{FBP GAP}{K6_IGAP} + \frac{GAP DHAP V_6f}{K6_eq V_6r}})

Component: TIM

TIM = \frac{V_7m DHAP}{K7_DHAP + DHAP + \frac{K7_DHAP}{K7_GAP} GAP} - (\frac{V_7m \frac{GAP}{K7_eq}}{K7_DHAP + DHAP + \frac{K7_DHAP}{K7_GAP} GAP})

Component: GAPDH

GAPDH = \frac{V_8m GAP NAD}{K8_GAP K8_NAD (1.0 + \frac{GAP}{K8_GAP} + \frac{BPG}{K8_BPG}) (1.0 + \frac{NAD}{K8_NAD} + \frac{NADH}{K8_NADH})} - (\frac{V_8m \frac{BPG NADH}{K8_eq}}{K8_GAP K8_NAD (1.0 + \frac{GAP}{K8_GAP} + \frac{BPG}{K8_BPG}) (1.0 + \frac{NAD}{K8_NAD} + \frac{NADH}{K8_NADH})})

Component: lpPEP

lpPEP = k9f BPG ADP - (k9r PEP ATP)

Component: PK

PK = \frac{V_10m ADP PEP}{(K10_PEP + PEP) (K10_ADP + ADP)}

Component: PDC

PDC = \frac{V_11m Pyr}{K11 + Pyr}

Component: ADH

ADH = \frac{V_12m ACA NADH}{(K12_NADH + NADH) (K12_ACA + ACA)}

Component: outEtOH

outEtOH = k0 EtOH_x

Component: difEtOH

difEtOH = \frac{k13}{y_vol} (EtOH - EtOH_x)

Component: lpGlyc

lpGlyc = \frac{V_15m DHAP}{K15_DHAP (1.0 + \frac{K15_INADH}{NADH} (1.0 + \frac{NAD}{K15_INAD})) + DHAP (1.0 + \frac{K15_NADH}{NADH} (1.0 + \frac{NAD}{K15_INAD}))}

Component: outGlyc

outGlyc = k0 Glyc_x

Component: difGlyc

difGlyc = \frac{k16}{y_vol} (Glyc - Glyc_x)

Component: outACA

outACA = k0 ACA_x

Component: difACA

difACA = \frac{k18}{y_vol} (ACA - ACA_x)

Component: lacto

lacto = k20 ACA_x CN_x

Component: inCN

inCN = k0 (CN_x_0 - CN_x)

Component: storage

storage = k22 ATP G6P

Component: consum

consum = k23 ATP

Component: AK

AK = k24f AMP ATP - (k24r {ADP}^{2.0})

Component: model_parameters

Source: Derived from workspace Hynne, Dano, Sorensen, 2001 at changeset ed0104aa0533.

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Full-scale model of glycolysis in Saccharomyces cerevisiae