Table 3. List of equations in the TI model, TI+AR model and gene network model.

Equation No.	Equation	Model
1	$\frac{\text{d}\left[x\right]}{\text{dt}}=k_x\text{-}\left(\mu +{\lambda }_x\right)[x]$	TI
2	$\frac{\text{d}\left[y\right]}{\text{dt}}=k_y\text{-}(\mu +{\lambda }_y)[y]$	TI
3	$\frac{\text{d}[x_{\text{k}}]}{\text{dt}}=k_x{}_{{}_{\text{k}}}\text{-}(\mu +{\lambda }_{x_{\text{k}}})[x_{\text{k}}]$	TI
4	$\frac{\text{d}[y_{\text{h}}]}{\text{dt}}=k_y{}_{{}_{\text{h}}}\text{-}(\mu +{\lambda }_{y_{\text{h}}})[y_{\text{h}}]$	TI
5	$\frac{\text{d}[x]}{\text{dt}}=k_x{\text{-k}}_{\text{b}xy}[x][y{]\text{-k}}_{\text{b}x{y}_{\text{h}}}[x][y_{\text{h}}{]+\text{k}}_{\text{u}xy}([x:y]+[x:y_{\text{h}}])\text{-}(\mu +{\lambda }_x)[x]$	TI+AR GN
6	$\frac{\text{d}[y]}{\text{dt}}=k_y{\text{-k}}_{\text{b}xy}[y][x{]\text{-k}}_{\text{b}{x}_{\text{k}}y}[y][x_{\text{k}}{]+\text{k}}_{\text{u}xy}([x:y]+[x_{\text{k}}:y])\text{-}(\mu +{\lambda }_y)[y]$	TI+AR GN
7	$\frac{\text{d}[x_{\text{k}}]}{\text{dt}}=k_{x_{\text{k}}}{\text{-k}}_{\text{b}{x}_{\text{k}}y}[x_{\text{k}}][y{]\text{-k}}_{\text{b}{x}_{\text{k}}{y}_{\text{h}}}[x_{\text{k}}][y_{\text{h}}{]+\text{k}}_{\text{u}xy}[x_{\text{k}}:y{]+\text{k}}_{\text{u}{x}_{\text{k}}{y}_{\text{h}}}[x_{\text{k}}:y_{\text{h}}]\text{-}(\mu +{\lambda }_{x_{\text{k}}})[x_{\text{k}}]$	TI+AR GN
8	$\frac{\text{d}[y_{\text{h}}]}{\text{dt}}=k_{y_{\text{h}}}{\text{-k}}_{\text{b}x{y}_{\text{h}}}[x][y_{\text{h}}{]\text{-k}}_{\text{b}{x}_{\text{k}}{y}_{\text{h}}}[x_{\text{k}}][y_{\text{h}}{]+\text{k}}_{\text{uxy}}[x:y_{\text{h}}{]+\text{k}}_{{\text{ux}}_{\text{k}}{\text{y}}_{\text{h}}}[x_{\text{k}}:y_{\text{h}}]\text{-}(\mu +{\lambda }_{y_{\text{h}}})[y_{\text{h}}]$	TI+AR GN
9	$\frac{\text{d}[x:y]}{\text{dt}}{=\text{k}}_{\text{b}xy}[x][y{]\text{-}(\text{k}}_{\text{u}xy}+\mu +{\lambda }_{x:y})[x:y]$	TI+AR GN
10	$\frac{\text{d}[x_{\text{k}}:y]}{\text{dt}}{=\text{k}}_{\text{b}{x}_{\text{k}}y}[x_{\text{k}}][y{]\text{-}(\text{k}}_{\text{u}xy}+\mu +{\lambda }_{x_{\text{k}}:y})[x_{\text{k}}:y]$	TI+AR GN
11	$\frac{\text{d}[x:y_{\text{h}}]}{\text{dt}}{=\text{k}}_{\text{b}x{y}_{\text{h}}}[x][y_{\text{h}}{]\text{-}(\text{k}}_{\text{u}xy}+\mu +{\lambda }_{x:y_{\text{h}}})[x:y_{\text{h}}]$	TI+AR GN
12	$\frac{\text{d}[x_{\text{k}}:y_{\text{h}}]}{\text{dt}}={\text{k}}_{\text{b}{x}_{\text{k}}{y}_{\text{h}}}[x_{\text{k}}][y_{\text{h}}{]\text{-}(\text{k}}_{\text{u}{x}_{\text{k}}{y}_{\text{h}}}+\mu +{\lambda }_{x_{\text{k}}:y_{\text{h}}})[x_{\text{k}}:y_{\text{h}}]$	TI+AR GN
13	$\frac{\text{d}[\text{X}]}{\text{dt}}{=\text{k}}_{\text{X}}[x{]\text{-k}}_{\text{XZ}}{[\text{X}][\text{Z}]+\text{k}}_{\text{uXZ}}[\text{X:Z}]\text{-}(\mu +{\lambda }_{\text{X}})[\text{X}]$	GN
14	$\frac{\text{d}[\text{Y}]}{\text{dt}}{=\text{k}}_{\text{Y}}[y]\text{-}(\mu +{\lambda }_{\text{Y}})[\text{Y}]$	GN
15	$\frac{\text{d}[\text{Z}]}{\text{dt}}{=\text{k}}_{\text{WZ}}{+\text{k}}_{\text{YZ}}{[\text{Y}]\text{-k}}_{\text{XZ}}{[\text{X}][\text{Z}]+\text{k}}_{\text{uXZ}}[\text{X:Z}]\text{-}(\mu +{\lambda }_{\text{Z}})[\text{Z}]$	GN
16	$\frac{\text{d}[\text{X:Z}]}{\text{dt}}{=\text{k}}_{\text{XZ}}{[\text{X}][\text{Z}]\text{-}(\text{k}}_{\text{uXZ}}+\mu +{\lambda }_{\text{XZ}})[\text{X:Z}]$	GN
17	$\frac{{[\text{O}}_{\text{Y}}]}{{[\text{O}}_{\text{Y,T}}]}=\frac{{\text{K}}_{\text{OY}}}{{\text{K}}_{\text{OY}}+[\text{X}]}$	GN
18	$f_{\text{Y}}=f_{\text{Y},\max }\frac{{[\text{O}}_{\text{Y}}]}{{[\text{O}}_{\text{Y,T}}]}+f_{\text{Y},\min }\left(1-\frac{{[\text{O}}_{\text{Y}}]}{{[\text{O}}_{\text{Y,T}}]}\right)$	GN