Team:HokkaidoU Japan/Promoter

From 2013.igem.org

(Difference between revisions)
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\begin{align*}
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\begin{align}
p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
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&=\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} } } \\
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&=\frac{ \frac{P}{N_{NS}} \exp\left(\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } }{1+\frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \right) \\
&\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} }
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\end{align*}
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\end{align}

Revision as of 17:04, 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{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } }{1+\frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \right) \\ &\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}