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Expression Model
From 2013.igem.org
(Difference between revisions)
| Line 9: | Line 9: | ||
[[File:ExpressionModel5.png|322px|center]] | [[File:ExpressionModel5.png|322px|center]] | ||
| - | + | system: | |
\begin{equation*} | \begin{equation*} | ||
[\text{Rec}]'=k_\text{syn}-k_\text{deg} [\text{Rec}] | [\text{Rec}]'=k_\text{syn}-k_\text{deg} [\text{Rec}] | ||
| + | \end{equation*} | ||
| + | solution: | ||
| + | \begin{equation*} | ||
| + | [\text{Rec}]=e^{-k_\text{deg}t}\Big([\text{Rec}]_0-\frac{k_\text{syn}}{k_\text{deg}}\Big)+\frac{k_\text{syn}}{k_\text{deg}} | ||
| + | \end{equation*} | ||
| + | steady state: | ||
| + | \begin{equation*} | ||
| + | [\text{Rec}]_\infty=\frac{k_\text{syn}}{k_\text{deg}} | ||
| + | \end{equation*} | ||
| + | calibration: | ||
| + | \begin{equation*} | ||
| + | k_\text{deg}=ln\Big(\frac{[\text{Rec}]_0-[\text{Rec}]_\infty}{[\text{Rec}]-[\text{Rec}]_\infty}\Big)\frac{1}{t} | ||
| + | \end{equation*} | ||
| + | \begin{equation*} | ||
| + | k_\text{syn}=ln\Big(\frac{[\text{Rec}]_0-[\text{Rec}]_\infty}{[\text{Rec}]-[\text{Rec}]_\infty}\Big)\frac{\text{[Rec}]_\infty}{t} | ||
\end{equation*} | \end{equation*} | ||
Revision as of 22:00, 6 September 2013
system: \begin{equation*} [\text{Rec}]'=k_\text{syn}-k_\text{deg} [\text{Rec}] \end{equation*} solution: \begin{equation*} [\text{Rec}]=e^{-k_\text{deg}t}\Big([\text{Rec}]_0-\frac{k_\text{syn}}{k_\text{deg}}\Big)+\frac{k_\text{syn}}{k_\text{deg}} \end{equation*} steady state: \begin{equation*} [\text{Rec}]_\infty=\frac{k_\text{syn}}{k_\text{deg}} \end{equation*} calibration: \begin{equation*} k_\text{deg}=ln\Big(\frac{[\text{Rec}]_0-[\text{Rec}]_\infty}{[\text{Rec}]-[\text{Rec}]_\infty}\Big)\frac{1}{t} \end{equation*} \begin{equation*} k_\text{syn}=ln\Big(\frac{[\text{Rec}]_0-[\text{Rec}]_\infty}{[\text{Rec}]-[\text{Rec}]_\infty}\Big)\frac{\text{[Rec}]_\infty}{t} \end{equation*}
