Table 3 Description of the model setup including mass balances for the sugars (glucose, xylose, and arabinose), enzyme E2, biomass, acetate, aqueous hydrogen, and aqueous carbon dioxide

Glu

(1 − Y _x )·Y_ac

(1 − Y _x )·\( Y_{{{\text{H}}_{2} }} \)

(1 − Y _x )·\( Y_{{{\text{CO}}_{2} }} \)

Y _x

\( \rho_{\text{Glu}} = k_{\text{m}} \cdot \frac{\text{Glu}}{{{\text{Glu}} + K_{\text{s,glu}} }} \cdot X \cdot v_{1} \)

Glu

(1 − Y _x )·Y_ac

(1 − Y _x )·\( Y_{{{\text{H}}_{2} }} \)

(1 − Y_x)·\( Y_{{{\text{CO}}_{2} }} \)

 − 1·E2

Y _x

\( \rho_{{{\text{Glu}},2}} = k_{{{\text{m}},2}} \cdot E2 \cdot \frac{\text{Glu}}{{{\text{Glu}} + K_{{{\text{s,glu}},2}} }} \cdot X \cdot v_{2} \)

Xyl

(1 − Y _x )·Y_ac

(1 − Y _x )·\( Y_{{{\text{H}}_{2} }} \)

(1 − Y _x )·\( Y_{{{\text{CO}}_{2} }} \)

Y _x

\( \rho_{\text{Xyl}} = k_{\text{m}} \cdot \frac{\text{Xyl}}{{{\text{Xyl}} + K_{\text{s,xyl}} }} \cdot X \cdot v_{1} \)

Ara

(1 − Y _x )·Y_ac

(1 − Y _x ) · \( Y_{{{\text{H}}_{2} }} \)

(1 − Y _x )·\( Y_{{{\text{CO}}_{2} }} \)

Y _x

\( \rho_{\text{Ara}} = k_{\text{m}} \cdot \frac{\text{Ara}}{{{\text{Ara}} + K_{\text{s,ara}} }} \cdot X \cdot v_{1} \)

Enzyme, E2 (synthesis)

\( \rho_{E} = \alpha \cdot \frac{{{\text{Glu}}^{n} }}{{{\text{Glu}}^{n} + K_{{{\text{s}},E2}}^{n} }} \cdot X \cdot u \)

Enzyme, E2 (decay)

\( \rho_{{{\text{dec,}}E2}} = \beta \cdot E2 \)

Biomass (decay)

Biomass (decay)

\( \rho_{{{\text{dec,}}X}} = r_{\text{cd}} \cdot X \)

\( v_{1} = \frac{{\rho_{\text{Xyl}} }}{{\hbox{max} \;\left( {\rho_{\text{Xyl}} ;\;\rho_{{{\text{Glu,}}2}} } \right)}} \)

\( v_{2} = \frac{{\rho_{{{\text{Glu}},2}} }}{{\hbox{max} \;\left( {\rho_{\text{Xyl}} ;\;\rho_{{{\text{Glu}},2}} } \right)}} \)

\( u = \frac{{\rho_{{{\text{Glu}},2}} }}{{{\text{sum }}\left( {\rho_{\text{Xyl}} ;\;\rho_{{{\text{Glu,}}2}} } \right)}} \)