Quantitative analysis of ultrasensitive responses

Ultrasensitive responses are common in cellular information transfer because they allow cells to decode extracellular stimuli in an all-or-none manner. Biochemical responses are usually analyzed by fitting the Hill equation, and the estimated Hill coefficient is taken as a measure of sensitivity. However, this approach is not appropriate if the response under consideration significantly deviates from the best-fit Hill equation. In addition, Hill coefficients greater than unity do not necessarily imply ultrasensitive behaviour if basal activation is significant. In order to circumvent these problems we propose a general method for the quantitative analysis of sensitivity, the relative amplification plot, which is based on the response coefficient defined in metabolic control analysis. To quantify sensitivity globally (i.e. over the whole stimulus range) we introduce the integral-based relative amplification coefficient. Our relative amplification approach can easily be extended to monotonically decreasing, bell-shaped or nonsaturated responses.