Table 2.

Kinetic rate expressions.

Benzoate transport:

$$r_{\mathit{BZT}}=r_{\mathit{BZT}}^{\mathit{max}}\frac{C_{\mathit{BEN}}^{\mathit{ex}}{C}_v}{\left(C_{\mathit{BEN}}^{\mathit{ex}}{C}_v+K_{\mathit{mBENT}}\right)\left(1+\frac{C_{\mathit{DIOL}}^{\mathit{in}}}{K_{\mathit{iBENT}}}\right)}$$ (19)

Benzoate 1,2-dioxygenase:

$$r_{\mathit{BDO}}=r_{\mathit{BDO}}^{\mathit{max}}\frac{C_{\mathit{BEN}}^{\mathit{in}}{C}_{l,O_2}{C}_v}{K_{\mathit{dBEN}}{K}_{\mathit{mb}{O}_2}+K_{\mathit{mBDO}}{C}_{l,O_2}{C}_v+K_{\mathit{mb}{O}_2}{C}_{\mathit{BEN}}^{\mathit{in}}+C_{\mathit{BEN}}^{\mathit{in}}{C}_{l,O_2}{C}_v}$$ (20)

Benzoate cis-diol dehydrogenase:

$$r_{\mathit{DIOLDH}}=r_{\mathit{DIOLDH}}^{\mathit{max}}\frac{C_{\mathit{DIOL}}^{\mathit{in}}}{{K_{\mathit{mDIOLDH}}\left(1+\frac{C_{\mathit{CAT}}^{\mathit{in}}}{K_{\mathit{iDIOLDH}}}\right)+C}_{\mathit{DIOL}}^{\mathit{in}}\left(1+\frac{K_{\mathit{mCATDH}}}{C_{\mathit{CAT}}^{\mathit{in}}}\right)}$$ (21)

Benzoate cis-diol transport:

$$r_{\mathit{DIOLT}}=r_{\mathit{DIOLT}}^{\mathit{max}}\left(\frac{C_{\mathit{DIOL}}^{\mathit{in}}}{C_{\mathit{DIOL}}^{\mathit{in}}+K_{\mathit{mDIOLTin}}}-\frac{{\left(C_{\mathit{DIOL}}^{\mathit{ex}}{C}_v\right)}^d}{{\left(C_{\mathit{DIOL}}^{\mathit{ex}}{C}_v\right)}^d+{\left(K_{\mathit{mDIOLTex}}\right)}^d}\right)$$ (22)

Catechol 1,2-dioxygenase:

$$r_{\mathit{CDO}}=r_{\mathit{CDO}}^{\mathit{max}}\frac{C_{\mathit{CAT}}^{\mathit{in}}{\left(1+\frac{C_{l,O_2}{C}_v}{K_{\mathit{mc}{O}_2}}\right)}^{n_{{\mathit{cO}}_2}}}{K_{\mathit{mCDO}}+C_{\mathit{CAT}}^{\mathit{in}}}$$ (23)

Catechol transport:

$$r_{\mathit{CT}}=r_{\mathit{CT}}^{\mathit{max}}\left(\frac{C_{\mathit{CAT}}^{\mathit{in}}}{C_{\mathit{CAT}}^{\mathit{in}}+K_{\mathit{mCTin}}}-\frac{{\left(C_{\mathit{CAT}}^{\mathit{ex}}{C}_v\right)}^c}{{\left(C_{\mathit{CAT}}^{\mathit{ex}}{C}_v\right)}^c+{\left(K_{\mathit{mCTex}}\right)}^c}\right)$$ (24)

Muconate isomerase:

$$r_{\mathit{MISO}}=r_{\mathit{MISO}}^{\mathit{max}}\frac{C_{\mathit{MUC}}^{\mathit{in}}\left(1-\frac{C_{\mathit{KAEL}}^{\mathit{in}}}{C_{\mathit{MUC}}^{\mathit{in}}{K}_{\mathit{eqMISO}}}\right)}{C_{\mathit{MUC}}^{\mathit{in}}+K_{\mathit{mMISO}}\left(1+\frac{C_{\mathit{KAEL}}^{\mathit{in}}}{K_{\mathit{mLISO}}}\right)}$$ (25)

β-Ketoadipate enol-lactone hydrolase:

$$r_{\mathit{LH}}=r_{\mathit{LH}}^{\mathit{max}}\frac{C_{\mathit{KAEL}}^{\mathit{in}}}{C_{\mathit{KAEL}}^{\mathit{in}}+K_{\mathit{mKAEL}}}$$ (26)

β-Ketoadipate succinyl-Co-A transferase:

$$r_{\mathit{KACOAT}}=r_{\mathit{KACOAT}}^{\mathit{max}}\frac{C_{\mathit{KA}}^{\mathit{in}}}{C_{\mathit{KA}}^{\mathit{in}}+K_{\mathit{mKACOAT}}}$$ (27)

cis,cis-Muconate transporta:

$r_{\mathit{MUCT}}=k_{\mathit{MUCT}}\mathit{z}\gamma \left(\frac{C_{\mathit{MHC}}^{\mathit{ex}}-C_{\mathit{MHC}}^{\mathit{in}}{e}^{z\gamma }}{1-e^{z\gamma }}\right)$ $$C_{\mathit{MHC}}^{\mathit{ex}}=\frac{C_{\mathit{MUC}}^{\mathit{ex}}{C}_v}{C_{\mathit{MUC}}^{\mathit{ex}}{C}_v+K_{\mathit{mMUCT}}}{C}_{\mathit{MHC}}^{\mathit{in}}=\frac{C_{\mathit{MUC}}^{\mathit{in}}}{C_{\mathit{MUC}}^{\mathit{in}}+K_{\mathit{mMUCT}}}$$ (28)

β-Ketoadipate transporta:

$r_{\mathit{KAT}}=k_{\mathit{KAT}}\mathit{z}\gamma \left(\frac{C_{\mathit{KHC}}^{\mathit{ex}}-C_{\mathit{KHC}}^{\mathit{in}}{e}^{z\gamma }}{1-e^{z\gamma }}\right)$ $$C_{\mathit{KHC}}^{\mathit{ex}}=\frac{C_{\mathit{KA}}^{\mathit{ex}}{C}_v}{C_{\mathit{KA}}^{\mathit{ex}}{C}_v+K_{\mathit{mKAT}}}{C}_{\mathit{KHC}}^{\mathit{in}}=\frac{C_{\mathit{KA}}^{\mathit{in}}}{C_{\mathit{KA}}^{\mathit{in}}+K_{\mathit{mKAT}}}$$ (29)

^aFor cis,cis-muconate and β-ketoadipate transport, $\text{z}\text{=-2}\text{; γ}\text{=}\frac{\text{∆ΨF}}{\text{RT}}\text{=-1.915}$; $C_v=\frac{{\rho }_x}{C_x}$.