Team:HokkaidoU Japan/Promoter

From 2013.igem.org

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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} }
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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 16:51, 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} } &\approx \frac{P}{N_{NS}} e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } &\propto e^{\frac{\epsilon_S - \epsilon_{NS}}{\kappa_BT} } \end{align} \(x=x+1\)