Team:HokkaidoU Japan/Promoter
From 2013.igem.org
Maestro E.coli
Promoter
\begin{align}
p&=\frac{W_{bound}}{W_{unbound}+W_{bound}} \\
&=\frac{ \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) }{1+\frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) } \\
\intertext{\mathrm{suppose\ that} \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) \ll 1 } \\
&\approx \frac{mathrm{P}}{mathrm{N}_{mathrm{N}S}} \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right) \\
&\propto \exp\left(\frac{\varepsilon_S - \varepsilon_{mathrm{N}S}}{\kappa_BT} \right)
\end{align}