Scale-invariant systems realize nonlinear differential operators

摘要

In recent years, several biomolecular systems have been shown to be scale-invariant (SI), i.e. to show the same output dynamics when exposed to geometrically scaled input signals (u → pu, p > 0) after pre-adaptation to accordingly scaled constant inputs. In this article, we show that SI systems-as well as systems invariant with respect to other input transformations-can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.