Team:HokkaidoU Japan/Promoter

From 2013.igem.org

(Difference between revisions)
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\begin{align*}
\begin{align*}
p&=\frac{W_{\mathrm{bound}}}{W_{\mathrm{unbound}}+W_{\mathrm{bound}}} \\[6pt]
p&=\frac{W_{\mathrm{bound}}}{W_{\mathrm{unbound}}+W_{\mathrm{bound}}} \\[6pt]
-
&=\frac{ \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) }{1+\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) } \\[6pt]
+
&=\frac{ \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) }{1+\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) } \\[6pt]
-
\mathrm{suppose\ that} &\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \ll 1 \\[6pt]
+
\mathrm{suppose\ that} &\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) \ll 1 \\[6pt]
-
&\approx \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \\[6pt]
+
&\approx \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) \\[6pt]
-
&\propto \exp\left(-\frac{\varepsilon_{-35}}{\kappa_{\mathrm{B}}T} \right)
+
&\propto \exp\left(-\frac{\varepsilon_{-35}}{k_{\mathrm{B}}T} \right)
\end{align*}
\end{align*}
\[
\[
-
p_i \propto \exp\left(-\frac{E_i}{\kappa_{\mathrm{B}}T}\right)
+
p_i \propto \exp\left(-\frac{E_i}{k_{\mathrm{B}}T}\right)
\]
\]

Revision as of 17:57, 26 September 2013

Maestro E.coli

Promoter

\begin{align*} p&=\frac{W_{\mathrm{bound}}}{W_{\mathrm{unbound}}+W_{\mathrm{bound}}} \\[6pt] &=\frac{ \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) }{1+\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) } \\[6pt] \mathrm{suppose\ that} &\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) \ll 1 \\[6pt] &\approx \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{k_{\mathrm{B}}T} \right) \\[6pt] &\propto \exp\left(-\frac{\varepsilon_{-35}}{k_{\mathrm{B}}T} \right) \end{align*} \[ p_i \propto \exp\left(-\frac{E_i}{k_{\mathrm{B}}T}\right) \] \[ \varepsilon_{\mathrm{bind}} = \Delta G = G_{\mathrm{bound} } - G_{\mathrm{unbound}} \]