You are here: Home / Exposures / Chassagnole, Rais, Quentin, Fell, Mazat, 2001 / An integrated study of Threonine-pathway enzyme kinetics in Escherichia coli

Model Mathematics

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Component: environment

Component: Asp

\frac{d}{d time} (Asp) = - vAKI - vAKIII

Component: aspp

\frac{d}{d time} (aspp) = vAKI + vAKIII - vASD

Component: ASA

\frac{d}{d time} (ASA) = vASD - vHDH

Component: hs

\frac{d}{d time} (hs) = vHDH - vHK

Component: hsp

\frac{d}{d time} (hsp) = vHK + vTS

Component: Thr

\frac{d}{d time} (Thr) = vTS

Component: ATP

\frac{d}{d time} (ATP) = - vAKI - vAKIII - vHK

Component: ADP

\frac{d}{d time} (ADP) = vAKI + vAKIII + vHK

Component: NADPH

\frac{d}{d time} (NADPH) = - vASD - vHDH

Component: NADP

\frac{d}{d time} (NADP) = vASD + vHDH

Component: Pi

\frac{d}{d time} (Pi) = vASD + vTS

Component: Lys

\frac{d}{d time} (Lys) = 0

Component: vAKI

vAKI = \frac{V_max_AK_I (Asp ATP - (\frac{aspp ADP}{K_eq}))}{(\frac{K_asp (1 + {(\frac{Thr}{K_iThr})}^{h_Thr})}{1 + {(\frac{Thr}{K_iThr alpha})}^{h_Thr}} + \frac{aspp K_asp}{K_aspp} + Asp) (K_ATP (1 + \frac{ADP}{K_ADP}) + ATP)}

Component: vASD

vASD = \frac{V_max_ASD (aspp NADPH - (\frac{ASA NADP Pi}{K_eq}))}{(K_aspp (1 + \frac{ASA}{K_ASA}) (1 + \frac{Pi}{K_Pi}) + aspp) (K_NADPH (1 + \frac{NADP}{K_NADP}) + NADPH)}

Component: vHDH

vHDH = \frac{V_max_HDH (ASA NADPH - (\frac{hs NADP}{K_eq}))}{\frac{1 + {(\frac{Thr}{K_iThr})}^{h}}{1 + {(\frac{Thr}{alpha K_iThr})}^{h}} (K_ASA + \frac{hs K_ASA}{K_hs} + ASA) (K_NADPH (1 + \frac{NADP}{K_NADP}) + NADPH)}

Component: vHK

vHK = \frac{V_max_HK hs ATP}{(\frac{K_hs (1 + \frac{ATP}{K_iATP})}{1 + \frac{Thr}{K_iThr}} + hs) (K_ATP (1 + \frac{hs}{K_ihs}) + ATP) (1 + \frac{Lys}{K_iLys})}

Component: vTS

vTS = \frac{V_max_TS hsp}{K_hsp + hsp}

Component: vAKIII

vAKIII = \frac{V_max_AK_III (Asp ATP - (\frac{aspp ADP}{K_eq}))}{(1 + {(\frac{Lys}{K_iLys})}^{h_Lys}) (K_asp (1 + \frac{aspp}{K_aspp}) + Asp) (K_ATP (1 + \frac{ADP}{K_ADP}) + ATP)}

Source: Derived from workspace Chassagnole, Rais, Quentin, Fell, Mazat, 2001 at changeset 690b04e1eaf5.

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An integrated study of Threonine-pathway enzyme kinetics in Escherichia coli