Team:HokkaidoU Japan/Projects/H Stem
From 2014.igem.org
(Difference between revisions)
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- | + | \[ X+Y \overset{k_{\rm unbind}}{\underset{k_{\rm bind}}{\rightleftharpoons}} Z \] | |
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- | \[ X+Y \overset{k_{unbind}}{\underset{k_{bind}}{\rightleftharpoons}} Z \] | + | |
\begin{cases} | \begin{cases} | ||
- | \dot{x}=a-bx-k_{\rm bind}xy+k_{unbind}z & \\ | + | \dot{x}=a-bx-k_{\rm bind}xy+k_{\rm unbind}z & \\ |
- | \dot{y}=1-y-k_{bind}xy+k_{unbind}z & \\ | + | \dot{y}=1-y-k_{\rm bind}xy+k_{\rm unbind}z & \\ |
- | \dot{z}=k_{bind}xy-k_{unbind}z-cz & | + | \dot{z}=k_{\rm bind}xy-k_{\rm unbind}z-cz & |
\end{cases} | \end{cases} | ||
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\[ y=\frac{1}{2} \biggl\{ \sqrt{ \bigl( a-1+\frac{b}{\gamma} \bigl)^2 +4 \frac{b}{\gamma}} - \Bigl( a-1+\frac{b}{\gamma} \Bigl) \biggl\} \] | \[ y=\frac{1}{2} \biggl\{ \sqrt{ \bigl( a-1+\frac{b}{\gamma} \bigl)^2 +4 \frac{b}{\gamma}} - \Bigl( a-1+\frac{b}{\gamma} \Bigl) \biggl\} \] | ||
- | \[ \gamma = \frac{k_{bind}c}{k_{unbind}+c} \] | + | \[ \gamma = \frac{k_{\rm bind}c}{k_{\rm unbind}+c} \] |
Revision as of 09:43, 13 October 2014
Over View
How To Use
Modelling
\[ X+Y \overset{k_{\rm unbind}}{\underset{k_{\rm bind}}{\rightleftharpoons}} Z \]
\begin{cases}
\dot{x}=a-bx-k_{\rm bind}xy+k_{\rm unbind}z & \\
\dot{y}=1-y-k_{\rm bind}xy+k_{\rm unbind}z & \\
\dot{z}=k_{\rm bind}xy-k_{\rm unbind}z-cz &
\end{cases}
\[ y=\frac{1}{2} \biggl\{ \sqrt{ \bigl( a-1+\frac{b}{\gamma} \bigl)^2 +4 \frac{b}{\gamma}} - \Bigl( a-1+\frac{b}{\gamma} \Bigl) \biggl\} \]
\[ \gamma = \frac{k_{\rm bind}c}{k_{\rm unbind}+c} \]