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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}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } }{1+\frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } } \\ | &=\frac{ \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } }{1+\frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } } \\ | ||
| - | &\mathrm{suppose that} \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \ll 1 \\ | + | &\mathrm{suppose\ that} \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \ll 1 \\ |
&\approx \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \\ | &\approx \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \\ | ||
&\propto e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } | &\propto e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } | ||
Revision as of 17:01, 26 September 2013
Maestro E.coli
Promoter
\begin{align*}
p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
&=\frac{ \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } }{1+\frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } } \\
&\mathrm{suppose\ that} \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \ll 1 \\
&\approx \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \\
&\propto e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} }
\end{align*}
