Team:HokkaidoU Japan/Promoter

From 2013.igem.org

(Difference between revisions)
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\begin{align}
\begin{align}
p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
-
&=\frac{ \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) }{1+\frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) } \\
+
&=\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) } \\
-
\intertext{\mathrm{suppose\ that} \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) \ll 1 } \\
+
&\mathrm{suppose\ that} \frac{P}{N_{\mathrm{NS}}} \exp\left(\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \ll 1 \\
-
&\approx \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) \\
+
&\approx \frac{P}{N_{\mathrm{NS}}} \exp\left(\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \\
-
&\propto \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right)
+
&\propto \exp\left(\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right)
\end{align}
\end{align}

Revision as of 17:15, 26 September 2013

Maestro E.coli

Promoter

\begin{align} p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\ &=\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) } \\ &\mathrm{suppose\ that} \frac{P}{N_{\mathrm{NS}}} \exp\left(\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \ll 1 \\ &\approx \frac{P}{N_{\mathrm{NS}}} \exp\left(\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \\ &\propto \exp\left(\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \end{align}