Figure 2.

The function used to transform the data and its effect on the Hill curve: (a) For low values, close to zero, the inverse softplus function (solid, red) approximates the logarithm (dashed, green). For high values, it approaches the identity line, $y=x$ (dotted, blue). (b) Where the logistic (Hill) function (dashed, red) has high values, the inverse softplus (solid, blue) leaves it almost unchanged. At low values, where the logistic function becomes close to a falling exponential, the inverse softplus transforms it to an almost straight line.