Combined Model
Introduction
Single cell model
Reactions
Equations
\begin{align*}
\frac{d[LacI]}{dt}&=\frac{a_\mathrm{LacI} \cdot (\frac{[Lact]_{out}}{K_\mathrm{M,appLact}})^{n_1}}{1+(\frac{[Lact]_{out}}{K_\mathrm{M,appLact}})^{n_1}}-d_{\mathrm{LacI}}[LacI]\\
\frac{d[LuxR]}{dt}&=\frac{a_\mathrm{LuxR} \cdot (\frac{[Lact]_{out}}{K_\mathrm{M,appLact}})^{n_1}}{1+(\frac{[Lact]_{out}}{K_\mathrm{M,appLact}})^{n_1}} \cdot \frac{1}{1+(\frac{[LacI]}{K_{\mathrm{R,LacI}}\cdot (\gamma_2+1)})^{n_\mathrm{2}}}-d_{\mathrm{LuxR}}[LuxR]\\
[LuxRAHL]&= \frac{[AHL]\cdot [LuxR]}{K_{\mathrm{d,LuxRAHL}}+[AHL]}\\
\frac{d[LuxI]}{dt}&=a_{\mathrm{LuxI}}k_{\mathrm{leaky}}([LuxR]-[LuxRAHL])+\frac{a_{\mathrm{LuxI}}(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}{1+(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}-d_{\mathrm{LuxI}}[LuxI]\\
\frac{d[AHL]}{dt}&=a_{\mathrm{AHL}}[LuxI]-d_{\mathrm{AHL}}[AHL]-\frac{v_\mathrm{Aiia}\cdot [AHL]}{K_{\mathrm{M,AiiA}}+[AHL]}\\
\frac{d[GFP]}{dt}&=a_\mathrm{GFP}k_{\mathrm{leaky}}([LuxR]-[LuxRAHL])+\frac{a_\mathrm{GFP}(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}{1+(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}-d_{\mathrm{GFP}}[GFP]\\
K_\mathrm{d-LuxRAHL} &= \frac{k_\mathrm{-LuxRAHL}}{k_\mathrm{LuxRAHL}}\\
\end{align*}
Simulation
