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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{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 \\ | ||
Revision as of 17:27, 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*}
