Finding the sensitivity of zero-order ultra sensitivity and its parameter dependence
I found the answer.
First, we need to find balanced equation for reaction. Then express the concentration of $xˆst$ in the steady state through E.
Then we can arrive to this kind of solution for the value of E.
$\displaystyle{E\frac{x_0 - \frac{x_o}{2}}{K + x_0 - \frac{x_0}{2}}} - {\frac{\frac{x_0}{2}}{K + \frac{x_0}{2}}} = 0.$
$\displaystyle{E\frac{\frac{x_0}{2}}{K + \frac{x_0}{2}}} - {\frac{\frac{x_0}{2}}{K + \frac{x_0}{2}}}= 0. $
E = 1