Scale invariance analysis for genetic networks applying homogeneity

Scalability is a property describing the change of the trajectory of a dynamical system under a scaling of the input stimulus and of the initial conditions. Particular cases of scalability include the scale invariance and fold change detection (when the scaling of the input does not influence the system output). In the present paper it is shown that homogeneous systems have this scalability property while locally homogeneous systems approximately possess this property. These facts are used for detecting scale invariance or approximate scalability (far from a steady state) in several biological systems. The results are illustrated by various regulatory networks.