Hill function ($x^n/(K^n+x^n)$)

A saturating response $x^n/(K^n+x^n)$, or its repressive complement $K^n/(K^n+x^n)$, with threshold $K>0$ and exponent $n>0$. In gene regulation these are phenomenological models of a regulator-dependent production rate; their sharp-threshold limit gives a logic approximation, but a fitted exponent need not count literal binding sites.