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# Table 2 Mathematical model for data generation

From: Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

Reactor model equations: | |
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\frac{dX(t)}{dt}=X(t)\xb7\mu (W(t))+D\xb7X(t) | \frac{dS(t)}{dt}=-{r}_{\text{s}}(S(t))\xb7X(t)-D\xb7(S(t)-{S}_{F}) |

\frac{dP(t)}{dt}={r}_{\rho}(W(t))\xb7X(t)-D\xb7P(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)\xb7\left({r}_{\text{s}}\xb7X(t)+\frac{{S}_{set}-S(t)}{{\tau}_{set}}\right) | D=\frac{F}{V} |

Cell model equations:
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\mu ={K}_{B\mathit{1}}\xb7\frac{W(t)}{{K}_{s}+W(t)}-{K}_{B\mathit{2}}\xb7{m}_{ATP} | {r}_{\rho}={K}_{\rho \mathit{1}}\xb7\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 \xb7\mathrm{exp}(-\tau /\beta )\xb7d\tau |