Team:HokkaidoU Japan/Promoter

From 2013.igem.org

(Difference between revisions)
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p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
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) } \\
&=\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 \\
+
\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) \\
&\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)
&\propto \exp\left(\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right)

Revision as of 17:24, 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*}