Table 2 Symbols used in the model equations

Initial feed rate

\(F_{0} = \left\{ {\begin{array}{*{20}l} {0,} & {t < t_{F} } \\ {\frac{{M_{F} \cdot \mu }}{{c_{F} \cdot y_{R} }},} & {t \ge t_{F} } \\ \end{array} } \right.\)

Glucose concentration

\(\left[ G \right] = \frac{G}{V}\)

Active metabolite mass

B = P + C _M

Glycolysis products concentration

\(\left[ P \right] = \frac{P}{(B + R) \cdot c}\)

Ethanol negative feedback

\(n_{E} = \sigma_{E}\cdot \frac{\left[ E \right]}{{\left[ E \right]_{max} }}\)

Lag phase

\(lag = 1 - \frac{{l_{1} }}{{1 + l_{2} \cdot { \exp }(l_{3} \cdot t)}}\)

Inhibitor negative feedback

\(n_{I} = \sigma_{I} \cdot\frac{[I]}{{[I]_{max} }}\)

Glucose effect

\(ge = \frac{1}{{1 + a \cdot { \exp }(b \cdot \left[ P \right])}}\)

Metabolic overflow

\(mo = 1 - ge\)

Ethanol concentration

\(\left[ E \right] = \frac{E}{V}\)

Maximum reserves

R _max  = (B + R) r _max

Death switch

\(d = \left\{ {\begin{array}{*{20}c} {0, \left[ P \right] \le \tau } \\ {1, \left[ P \right] > \tau } \\ \end{array} } \right.\)

Medium volume in the reactor

\(V(t) = \left\{\begin{array}{ll} V_{0},& t < t_{F} \\ \frac{{M_{F} }}{{c_{F} \cdot y_{R} }}\cdot exp(\mu \cdot (t - t_{F} )), &t_{F} \le t \le t_{END}\\ \end{array} \right.\)