Team:Rice/Model/CircuitOutput
Circuit Expression
Overview
The model includes host expression of a circuit gene, with transcription and translation by host machinery. Since our circuits have fluorescent reporter proteins, we should be able to correlate circuit expression levels in the model with fluorescence levels from wet lab data.
Explanation
Note: if the equations below seem messed up, please follow this link to a simplified version of this page.
Circuit proteins includes both mCherry and the tetR repressor proteins. We simulate the creation of these molecules just like we simulate other host proteins, adding equations for their mRNAs ($m_C$), ribosomal complexes ($c_C$), and the actual proteins $p_C$. The number of circuit proteins in the cell provides a good measure of the expected fluorescence of the cells.
Equations
\begin{equation*} \begin{aligned} \frac{dm_C}{dt} &= \alpha w_C \frac{E_c}{E_c+o_C} + \gamma \frac{c_C}{n_C} - b_r R_h m_C + u_r c_C - (d_r+\lambda) m_C \\ \frac{dc_C}{dt} &= b_r R_h m_C - u_r c_C - \gamma \frac{c_C}{n_C} - \lambda c_C \\ \frac{dp_C}{dt} &= \gamma \frac{c_C}{n_C} - \lambda p_C \\ \end{aligned} \end{equation*}