Parameter sensitivity of autorepressed expression
= Parameter sensitivity of autorepressed expression
{title2=$S_{Y,\beta}=(1+s)/[1+(n+1)s]$}
At a <Hill equation> equilibrium with $s=(Y/K)^n$, differentiating $\beta=\alpha Y(1+s)$ gives the displayed logarithmic sensitivity. It approaches one without effective feedback and $1/(n+1)$ under strong repression. Threshold pinning in the <logic approximation for gene regulation> instead gives approximately zero production sensitivity while the threshold is held fixed.