text: Consider two coupled ultrasensitive modules, disregarding effects of sequestration of molecular components between layers. In this case, the expression for the system's dose-response curve, , results from the mathematical composition of the functions, , which describe the input/output relationship of isolated modules :
  Brown et al. (1997)  have shown that the local ultrasensitivity of the different layers combines multiplicatively:
  In connection with this result, Ferrell et al. (1997)  showed, for Hill-type modules, that the overall cascade global ultrasensitivity had to be less than or equal to the product of the global ultrasensitivity estimations of each cascade's layer,
  where  and  are the Hill coefficient of modules 1 and 2 respectively.
  Altszyler et al. (2017)  have shown that the cascade's global ultrasensitivity can be analytically calculated:
  where  and  delimited the Hill inputs working range of the composite system, i.e. the input values for the i-layer so that the last layer (corresponding to  in this case) reached the 10% and 90% of it maximal output level. It followed this equation that the systems Hill coefficient  could be written as the product of two factors,   and , which characterized local average sensitivities over the relevant input region for each layer: , with  in this case.
  For the more general case of a cascade of  modules, the Hill Coefficient can be expressed as: