Modeling

\begin{equation} \large \frac{d[mRNA_{Luc}]}{dt} = \alpha _{mLuc}\cdot (pro_{ars})\cdot(\frac{k_{D1}^{h_{1}}}{k_{D1}^{h_{1}}+[ArsR]^{h_{1}}})- \delta _{mRNA_{Luc}}[mRNA_{Luc}] \end{equation}

\begin{equation} \large \frac{d[Luc]}{dt} = \alpha _{pLuc}\cdot[mRNA_{Luc}]- \delta _{Luc}[Luc] \end{equation}