\begin{align*} p&=\frac{W_{\mathrm{bound}}}{W_{\mathrm{unbound}}+W_{\mathrm{bound}}} \\[6pt] &=\frac{ \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) }{1+\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) } \\[6pt] \mathrm{suppose\ that} &\frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \ll 1 \\[6pt] &\approx \frac{P}{N_{\mathrm{NS}}} \exp\left(-\frac{\varepsilon_{\mathrm{S}} - \varepsilon_{\mathrm{NS}}}{\kappa_{\mathrm{B}}T} \right) \\[6pt] &\propto \exp\left(-\frac{\varepsilon_{-35}}{\kappa_{\mathrm{B}}T} \right) \end{align*} \[ p_i \propto \exp\left(-\frac{E_i}{\kappa_{\mathrm{B}}T}\right) \] \[ \varepsilon_{\mathrm{bind}} = \DeltaG = G_{\mathrm{bound} } - G_{\mathrm{unbound}} \]