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

Reactor model equations: | |
---|---|

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

$\frac{dP(t)}{dt}={r}_{\rho}(W(t))\xb7X(t)-D\xb7P(t)$ | $\frac{dV(t)}{dt}=F(t)$ |

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

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

Cell model equations:
| |

$\mu ={K}_{B\mathit{1}}\xb7\frac{W(t)}{{K}_{s}+W(t)}-{K}_{B\mathit{2}}\xb7{m}_{ATP}$ | ${r}_{\rho}={K}_{\rho \mathit{1}}\xb7\mu +{K}_{\rho \mathit{2}}$ |

${r}_{S}={r}_{S,max}\cdot \frac{S(t)}{{K}_{s}+S(t)}$ | $W(t)={\displaystyle {\int}_{-\infty}^{t}(S}(t-\tau )/{\beta}^{2}).\tau \xb7\mathrm{exp}(-\tau /\beta )\xb7d\tau $ |