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\frac{dr}{dt} &= k_{fr} r_{uf} - k_r r \\ | \frac{dr}{dt} &= k_{fr} r_{uf} - k_r r \\ | ||
\end{align} | \end{align} | ||
+ | |||
+ | |||
+ | |||
+ | Where $a=$ Concentration of AraC protein, $r=$ Concentration of LacI protein. | ||
+ | $\tau_a$,$\tau_r$ are parameters dependent on various constants as follows- | ||
+ | |||
+ | %\[\displaystyle{\tau_y = \frac{m_1}{m_2} \sqrt[4]{\frac{k_1^2 k_{da}^2}{k_2 k_{dr_1} k_{dr_2}}}}\] | ||
+ | \[c_a = {k_1 k_{da}}\] | ||
+ | \[c_r = {k_2 {k_{dr_1}^2} k_{dr_2}}\] | ||
+ | $k_1,k_2$ are dependent on IPTG and Arabinose concentration, given by- | ||
+ | \[k_1 = \frac{[ara]^2}{[ara]^2 + (2.5^2)} .\frac{1}{1 + (\frac{[iptg]}{1.8})^2}\] | ||
+ | \[k_2 = 2*(0.19 . \frac{1}{1 + (\frac{[iptg]}{0.035})^2} + 0.01)\] | ||
+ | \\ | ||
+ | |||
+ | \begin{tabular}{|c|c|c|c|c|} | ||
+ | \hline | ||
+ | Sr. & Parameter & Description & value & units \\ \hline | ||
+ | 1 & $ \gamma_{ma}, \gamma_{mr} $ & Degradation rate of AraC/LacI mRNA & 0.54 & $min^{-1}$ \\ \hline | ||
+ | |||
+ | 2 & $b_a,b_r$ & Transcription rate of AraC, LacI genes & 0.36 & $min^{-1}$ \\ \hline | ||
+ | 3 & $ \alpha$ & Increased transcription rate Due to AraC binding & 20 & \\ \hline | ||
+ | |||
+ | 4 & $t_{a}$ & rate of transcription of AraC & 90 & $min^{-1}$ \\ \hline | ||
+ | 5 & $t_{r}$ & rate of transcription of LacI & 90 & $min^{-1}$ \\ \hline | ||
+ | 6 & $k_{a}$ & Rate of degradation of AraC protein & 0.455 & $min^{-1}$ \\ \hline | ||
+ | 7 & $k_{r}$ & Rate of degradation of LacI protein & 0.182 & $min^{-1}$ \\ \hline | ||
+ | 8 & $k_{da}$ & AraC dimerisation constant & 100 & $molecules^{-1}$ \\ \hline | ||
+ | 9 & $k_{dr1}$ & LacI dimerisation constant & 100 & $molecules^{-1}$ \\ \hline | ||
+ | 10 & $k_{dr2}$ & LacI tetramerisation constant & 100 & $molecules^{-1}$ \\ \hline | ||
+ | \end{tabular} | ||
+ | |||
<br /> | <br /> |
Revision as of 14:25, 24 October 2017
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