Table 2 Mathematical model for data generation

$\frac{dX(t)}{dt}=X(t)·\mu (W(t))+D·X(t)$

$\frac{dS(t)}{dt}=-r_{\text{s}}(S(t))·X(t)-D·(S(t)-S_F)$

$\frac{dP(t)}{dt}=r_{\rho }(W(t))·X(t)-D·P(t)$

$\frac{dV(t)}{dt}=F(t)$

$\frac{dW}{dt}=\frac{Z-W}{\beta }$

$\frac{dZ}{dt}=\frac{S(t)-Z}{\beta }$

$F(t)=\left(\frac{V(t)}{S_F-S(t)}\right)·\left(r_{\text{s}}·X(t)+\frac{S_{set}-S(t)}{{\tau }_{set}}\right)$

$D=\frac{F}{V}$

Cell model equations:

$\mu =K_{B\mathit{1}}·\frac{W(t)}{K_s+W(t)}-K_{B\mathit{2}}·m_{ATP}$

$r_{\rho }=K_{\rho \mathit{1}}·\mu +K_{\rho \mathit{2}}$

$r_S=r_{S,max}\cdot \frac{S(t)}{K_s+S(t)}$

$W(t)={\displaystyle {\int }_{-\infty }^t(S}(t-\tau )/{\beta }^2).\tau ·\exp (-\tau /\beta )·d\tau$