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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_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) }{1+\frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) } \\ | &=\frac{ \frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) }{1+\frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) } \\ | ||
| - | &\mathrm{suppose\ that} \frac{P}{N_{NS}} | + | &\mathrm{suppose\ that} \frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) \ll 1 \\ |
| - | &\approx \frac{P}{N_{NS}} | + | &\approx \frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) \\ |
| - | &\propto | + | &\propto \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) |
\end{align} | \end{align} | ||
| - | |||
Revision as of 17:07, 26 September 2013
Maestro E.coli
Promoter
\begin{align}
p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
&=\frac{ \frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) }{1+\frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) } \\
&\mathrm{suppose\ that} \frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) \ll 1 \\
&\approx \frac{P}{N_{NS}} \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right) \\
&\propto \exp\left(\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} \right)
\end{align}
