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Model Mathematics

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Component: environment

Component: G_o

Component: G

\frac{d}{d time} (G) = V_IN - V_HK

Component: G6P

\frac{d}{d time} (G6P) = V_HK - (V_PFK + V_G6PDH)

Component: FDP

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

Component: G3P

\frac{d}{d time} (G3P) = 2 V_ALD - V_GAPDH

Component: DPG

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

Component: PEP

\frac{d}{d time} (PEP) = V_PGK - V_PK

Component: Py

\frac{d}{d time} (Py) = V_PK - (V_TCA + V_ADH)

Component: ATP

\frac{d}{d time} (ATP) = V_PGK + V_PK + PO V_TCA - (V_HK + V_PFK + V_ATPase)

Component: ADP

ADP = Cn - (ATP + AMP)

Component: AMP

Component: GTP

Component: GDP

Component: H

Component: NADP

Component: NADH

Component: NAD

Component: CD

CD = CMTP - (CT + CP)

Component: CT

\frac{d}{d time} (CT) = - (kpol CT {CP}^{2} + kf CD + kb CT GDP)

Component: CP

\frac{d}{d time} (CP) = kpol CT {CP}^{2} - (kdp CP)

Component: PKp

\frac{d}{d time} (PKp) = 0.1 kp2 PKt CP - (kp3 PKp + k4 PKp GTP)

Component: PKt

PKt = C_PK - PKp

Component: V_IN

V_IN = V_IN_max (\frac{G_o}{(KG_in + G_o) (1 + \frac{G6P}{Ke_in})} - (\frac{G}{(KG_in + G) (1 + \frac{G6P}{Ke_in})}))

Component: V_HK

V_HK = \frac{V_HK_max 1}{1 + \frac{KG_s KATP_m}{G ATP} + \frac{KG_m}{G} + \frac{KATP_m}{ATP}}

Component: V_PFK

V_PFK = \frac{\frac{\frac{V_PFK_max gr G6P}{KG6P_r} ATP}{KATP_r} {(1 + \frac{G6P}{KG6P_r} + \frac{ATP}{KATP_r} + \frac{\frac{gr G6P}{KG6P_r} ATP}{KATP_r})}^{n1 - 1}}{{(1 + \frac{G6P}{KG6P_r} + \frac{ATP}{KATP_r} + \frac{\frac{gr G6P}{KG6P_r} ATP}{KATP_r})}^{n1} + Lo {(\frac{1 + \frac{cAMP AMP}{KAMP_r}}{1 + \frac{AMP}{KAMP_r}})}^{n1} {(1 + \frac{cG6P G6P}{KG6P_r} + \frac{cATP ATP}{KATP_r} + \frac{\frac{gr cG6P G6P}{KG6P_r} cATP ATP}{KATP_r})}^{n1}}

Component: V_G6PDH

V_G6PDH = \frac{V_G6PDH_max}{\frac{KG6P KNADP}{G6P NADP} + \frac{KG6P}{G6P} + \frac{KNADP}{NADP} + 1} + \frac{V_G6PDH_max_II}{\frac{KG6P KNADP_KTUB}{G6P NADP TUB} + \frac{KG6P KNADP_}{G6P NADP} + \frac{KNADP_KTUB}{NADP TUB} + \frac{KG6P KTUB}{G6P TUB} + \frac{KTUB}{TUB} + \frac{KG6P}{G6P} + \frac{KNADP_}{NADP} + 1} TUB = CT + CD

Component: V_ALD

V_ALD = \frac{\frac{V_ALD_max FDP}{KFDP_m} - (\frac{V_ALD_max_r G3P}{KG3P_m})}{1 + \frac{FDP}{KFDP_m} + \frac{G3P}{KG3P_m}}

Component: V_GAPDH

V_GAPDH = \frac{V_GAPDH_max}{1 + \frac{KG3P}{G3P} + \frac{KNAD}{NAD} (1 + \frac{AMP}{K1} + \frac{ADP}{K2} + \frac{ATP}{K3}) + \frac{KG3P KNAD}{G3P NAD} (1 + \frac{NADH}{KNADH_i}) + 1 + \frac{AMP}{K1} + \frac{ADP}{K2} + \frac{ATP}{K3}}

Component: V_PGK

V_PGK = \frac{V_PGK_max DPG}{KDPG_m + DPG}

Component: V_PK

V_PK = \frac{\frac{V_PK_max}{1 + \frac{KpH}{H}} (gr_PK \frac{PEP}{KPEP_r} \frac{ADP}{KADP_r} R^{n - 1} + Lo_PK {(\frac{1 + \frac{cFDP FDP}{KFDP_r}}{1 + \frac{FDP}{KFDP_r}})}^{n} \frac{FDP}{KFDP_r} gt_PK \frac{cPEP PEP}{KPEP_r} \frac{cADP ADP}{KADP_r} T^{n - 1})}{R^{n} + Lo_PK {(\frac{1 + \frac{cFDP FDP}{KFDP_r}}{1 + \frac{FDP}{KFDP_r}})}^{n} T^{n}} R = 1 + \frac{PEP}{KPEP_r} + \frac{ADP}{KADP_r} + \frac{\frac{gr_PK PEP}{KPEP_r} ADP}{KADP_r} T = 1 + \frac{cPEP PEP}{KPEP_r} + \frac{cADP ADP}{KADP_r} + \frac{\frac{gt_PK cPEP PEP}{KPEP_r} cADP ADP}{KADP_r} V_PK_max = V_PKt_max + \frac{(V_PKp_max - V_PKt_max) PKp}{C_PK} n = 4 + \frac{PKp}{C_PK}

Component: V_TCA

V_TCA = \frac{V_TCA_max {Py}^{2}}{{KPy_m}^{2} + {Py}^{2}}

Component: V_ADH

V_ADH = \frac{V_ADH_max Py}{KPy__m + Py}

Component: V_ATPase

V_ATPase = KATP ATP

Source: Derived from workspace Aon, Cortassa, 2002 at changeset 6a5e3ad9eaef.

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Coherent and robust modulation of a metabolic network by cytoskeletal organization and dynamics