An increasing Hill coefficient, k , causes logarithmic sensitivity to low input signals. At k=1 (left curve), the sensitivity is linear with a steady increase in output even at very low input levels, implying infinite precision. As k increases, sensitivity at low input declines, and the required threshold input level becomes higher and sharper to induce an output response of 1% of the maximum (y=0.01). The curves of increasing slope correspond to k=1,2,4,8 in Eq. (4), with logarithmic scaling of the input x plotted here.