. 2015 Mar 21;68(4):1019–1032. doi: 10.1007/s10616-015-9858-9

Table 2.

Model equations used in the tool simplified to batch mode

Balance equations	Kinetics
Biophase	Growth/death
$\frac{d X_{v}}{d t} = (μ - μ_{d}) \cdot X_{v} (1)$	$μ = μ_{max} \cdot \frac{c_{G l c}}{c_{G l c} + K_{S, G l c}} \cdot \frac{c_{G l n}}{c_{G ln} + K_{S, G l n}} (7)$
$\frac{d X_{t}}{d t} = μ \cdot X_{v} - K_{L y s} \cdot (X_{t} - X_{v}) (2)$	$μ_{d} = μ_{d, min} + μ_{d, max} \cdot \frac{K_{S, G l c}}{K_{S, G l c} + c_{G l c}} (8)$
Liquid phase	Substrate uptake/metabolite production
$\frac{d c_{G l c}}{d t} = - q_{G l c} \cdot X_{v} (3)$	$q_{G l c} = q_{G l c, max} \cdot \frac{c_{G l c}}{c_{G l c} + k_{G l c}} \cdot (\frac{μ}{μ + μ_{max}} + 0.5) (9)$
$\frac{d c_{G l n}}{d t} = - q_{G l n} \cdot X_{v} (4)$	$q_{G l n} = q_{G l n, m a x} \cdot \frac{c_{G l n}}{c_{G l n} + k_{G l n}} (10)$
$\frac{d c_{L a c}}{d t} = q_{L a c} \cdot X_{v} (5)$	$\begin{matrix} q_{L a c} = Y_{L a c / G l c} \cdot \frac{c_{G l c}}{c_{L a c}} \cdot q_{G l c} - q_{L a c, u p t a k e} \\ c_{G l c} \geq 0.5 m M : q_{L a c, u p t a k e} = 0 \\ c_{G l c} < 0.5 m M : q_{L a c, u p t a k e} = q_{L a c, u p t a k e, max} (11) \end{matrix}$
$\frac{d c_{A m m}}{d t} = q_{A m m} \cdot X_{v} (6)$	$q_{A m m} = Y_{A m m / G l n} \cdot q_{G l n} (12)$