Global sensitivity measures such as the Hill coefficient do not characterise the local behaviours of the s-shaped curves. Instead, these features are well captured by the response coefficient measure  defined as:
In systems biology, such system responses are referred to as control coefficients. Specifically, the concentration control coefficients measure the response of concentrations to changes in a given input. In addition, within the framework of the more general biochemical control analysis, such responses can be described in terms of the individual local responses, called the elasticities.