Team:HokkaidoU Japan/Promoter

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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}} e^{\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} } \ll 1 \\ &\approx \frac{P}{N_{NS}} e^{\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} } \\ &\propto e^{\frac{\varepsilon_S - \varepsilon_{NS}}{\kappa_BT} } \end{align}