Cumulative dose responses for adapting biological systems

This paper introduces the notion of cumulative dose response (cDR). The cDR is the area under the plot of a response variable, an integral taken over a fixed time interval and seen as a function of an input parameter. This work was motivated by the accumulation of cytokines resulting from T cell stimulation, where a non-monotonic cDR has been observed experimentally. However, the notion is of general applicability. A surprising conclusion is that incoherent feedforward loops studied in the systems biology literature, though capable of non-monotonic dose responses, can be mathematically shown to always result in monotonic cDR.